%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU565^1 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:35:18 AM UTC 2026
% Result : Theorem 2.43s 1.58s
% Output : Refutation 2.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 4
% Syntax : Number of formulae : 31 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 1781 ( 494 equ; 0 cnn)
% Maximal formula atoms : 84 ( 57 avg)
% Number of connectives : 947 ( 57 ~; 28 |; 266 &; 170 @)
% ( 3 <=>; 423 =>; 0 <=; 0 <~>)
% Maximal formula depth : 91 ( 26 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 197 ( 194 usr; 89 con; 0-4 aty)
% Number of variables : 64 ( 0 ^; 46 !; 18 ?; 64 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
exu: ( $i > $o ) > $o ).
thf(func_def_6,type,
setadjoin: $i > $i > $i ).
thf(func_def_8,type,
powerset: $i > $i ).
thf(func_def_10,type,
setunion: $i > $i ).
thf(func_def_19,type,
descr: ( $i > $o ) > $i ).
thf(func_def_21,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_26,type,
prop2set: $o > $i ).
thf(func_def_36,type,
nonempty: $i > $o ).
thf(func_def_69,type,
set2prop: $i > $o ).
thf(func_def_88,type,
subset: $i > $i > $o ).
thf(func_def_89,type,
disjoint: $i > $i > $o ).
thf(func_def_90,type,
setsmeet: $i > $i > $o ).
thf(func_def_110,type,
sP1: $i > $i > $o ).
thf(func_def_111,type,
sP2: $i > $o ).
thf(func_def_112,type,
sP3: $i > $i > $o ).
thf(func_def_113,type,
sP4: $i > $i > $o ).
thf(func_def_115,type,
sK6: $i > $i ).
thf(func_def_118,type,
sK9: $i > $o ).
thf(func_def_121,type,
sK12: $i > $i > $o ).
thf(func_def_122,type,
sK13: $i > $i ).
thf(func_def_123,type,
sK14: $i > $i ).
thf(func_def_124,type,
sK15: ( $i > $i > $o ) > $i > $i ).
thf(func_def_125,type,
sK16: ( $i > $i > $o ) > $i > $i ).
thf(func_def_126,type,
sK17: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_127,type,
sK18: $i > $o ).
thf(func_def_128,type,
sK19: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_129,type,
sK20: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_132,type,
sK23: $i > $o ).
thf(func_def_133,type,
sK24: $i > $o ).
thf(func_def_140,type,
sK31: $i > $i > $i ).
thf(func_def_142,type,
sK33: $i > $i ).
thf(func_def_146,type,
sK37: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_147,type,
sK38: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_148,type,
sK39: $i > $o ).
thf(func_def_149,type,
sK40: $i > $o ).
thf(func_def_156,type,
sK47: $i > $i ).
thf(func_def_162,type,
sK53: ( $i > $o ) > $i ).
thf(func_def_163,type,
sK54: $i > $o ).
thf(func_def_171,type,
sK62: ( $i > $o ) > $i ).
thf(func_def_172,type,
sK63: $i > $o ).
thf(func_def_173,type,
sK64: $i > $i ).
thf(func_def_174,type,
sK65: $i > $o ).
thf(func_def_178,type,
sK69: $i > $i > $i ).
thf(func_def_184,type,
sK75: $i > $o ).
thf(func_def_185,type,
sK76: $i > ( $i > $o ) > $i ).
thf(func_def_186,type,
sK77: $i > $o ).
thf(func_def_189,type,
sK80: $i > $i > $i ).
thf(func_def_190,type,
sK81: $i > $i > $i ).
thf(func_def_193,type,
sK84: $i > $o ).
thf(func_def_195,type,
sK86: $i > ( $i > $o ) > $i ).
thf(func_def_205,type,
sK96: $i > $i ).
thf(func_def_207,type,
sK98: $i > $i ).
thf(func_def_208,type,
sK99: $i > $i > $i ).
thf(func_def_213,type,
sK104: $i > $i > $i ).
thf(func_def_220,type,
sK111: $i > $o ).
thf(func_def_226,type,
sK117: $i > $o ).
thf(func_def_228,type,
sK119: ( $i > $o ) > $i > $i ).
thf(func_def_231,type,
sK122: $i > $o ).
thf(func_def_232,type,
sK123: $i > $i ).
thf(func_def_233,type,
sK124: ( $i > $o ) > $i ).
thf(func_def_237,type,
sK128: $i > $o ).
thf(func_def_242,type,
sK133: $i > $i > $i ).
thf(func_def_243,type,
sK134: $i > $i > $i ).
thf(func_def_244,type,
sK135: $i > $i > $i ).
thf(func_def_245,type,
sK136: $i > $i > $i ).
thf(func_def_246,type,
sK137: $i > $i > $i > $i ).
thf(func_def_247,type,
sK138: $i > $i ).
thf(func_def_248,type,
sK139: $i > $i ).
thf(func_def_249,type,
sK140: $i > $i ).
thf(func_def_250,type,
sK141: $i > $i ).
thf(func_def_251,type,
sK142: $i > $i > $i > $i ).
thf(func_def_252,type,
sK143: $i > $i > $i > $i ).
thf(func_def_253,type,
sK144: $i > $i > $i ).
thf(func_def_254,type,
sK145: $i > $i > $i ).
thf(func_def_255,type,
sK146: $i > $i > $i ).
thf(func_def_257,type,
sK148: $i > $i ).
thf(func_def_258,type,
sK149: $i > $i ).
thf(func_def_259,type,
sK150: $i > $i ).
thf(func_def_260,type,
sK151: $i > $i > $i ).
thf(func_def_261,type,
sK152: $i > $o ).
thf(func_def_263,type,
sK154: $i > ( $i > $o ) > $i ).
thf(func_def_265,type,
sK156: $i > $o ).
thf(func_def_267,type,
sK158: ( $i > $o ) > $i > $i ).
thf(func_def_269,type,
sK160: $i > $o ).
thf(func_def_271,type,
sK162: $i > $o ).
thf(func_def_277,type,
sK168: $i > $i > $i ).
thf(func_def_283,type,
sK174: $i > $o ).
thf(func_def_285,type,
sK176: ( $i > $o ) > $i > $i ).
thf(func_def_289,type,
sK180: $i > $o ).
thf(func_def_291,type,
sK182: ( $i > $o ) > $i ).
thf(func_def_292,type,
sK183: ( $i > $o ) > $i ).
thf(func_def_294,type,
sK185: $i > $o ).
thf(func_def_296,type,
sK187: $i > $i ).
thf(func_def_298,type,
sK189: $i > $i ).
thf(func_def_301,type,
sK192: $i > $o ).
thf(func_def_304,type,
sK195: $i > $o ).
thf(func_def_305,type,
sK196: $i > $o ).
thf(func_def_306,type,
sK197: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_307,type,
sK198: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_314,type,
sK205: $o > $i > $i > $i ).
thf(func_def_315,type,
sK206: $i > $o ).
thf(func_def_318,type,
sK209: $i > ( $i > $o ) > $i ).
thf(func_def_321,type,
sK212: $i > $i > $i ).
thf(func_def_329,type,
sK220: ( $i > $o ) > $i > $i ).
thf(func_def_331,type,
sK222: $i > $o ).
thf(func_def_347,type,
ph238:
!>[X0: $tType] : X0 ).
thf(f1634,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f1626]) ).
thf(f1626,plain,
$true != $true,
inference(superposition,[status(thm)],[f1302,f835]) ).
thf(f835,plain,
( $true
= ( in @ sK25 @ sK26 ) ),
inference(cnf_transformation,[status(thm)],[f401]) ).
thf(f401,plain,
( ( setadjoinAx = $true )
& ( exu__Cong = $true )
& ( setunionI = $true )
& ( nonemptyI = $true )
& ( prop2set2propI = $true )
& ( setbeta = $true )
& ( exuE3u = $true )
& ( powerset__Cong = $true )
& ( upairsetE = $true )
& ( exuEu = $true )
& ( prop2setI = $true )
& ( exuI1 = $true )
& ( emptyinunitempty = $true )
& ( quantDeMorgan3 = $true )
& ( nonemptyE1 = $true )
& ( nonemptyI1 = $true )
& ( setadjoinIR = $true )
& ( exuE3e = $true )
& ( notinsingleton = $true )
& ( setunionAx = $true )
& ( emptysetsubset = $true )
& ( nonemptyImpWitness = $true )
& ( prop2setE = $true )
& ( setadjoinOr = $true )
& ( omegaIndAx = $true )
& ( powersetAx = $true )
& ( dsetconstr__Cong = $true )
& ( vacuousDall = $true )
& ( eqinunit = $true )
& ( quantDeMorgan1 = $true )
& ( emptyE1 = $true )
& ( notdallE = $true )
& ( emptyI = $true )
& ( notinemptyset = $true )
& ( wellorderingAx = $true )
& ( dsetconstrEL = $true )
& ( in__Cong = $true )
& ( descrp = $true )
& ( foundationAx = $true )
& ( emptysetE = $true )
& ( dsetconstrI = $true )
& ( omega0Ax = $true )
& ( noeltsimpempty = $true )
& ( uniqinunit = $true )
& ( emptysetAx = $true )
& ( emptyset__Cong = $true )
& ( setadjoinIL = $true )
& ( exuI3 = $true )
& ( subsetE = $true )
& ( eqimpsubset2 = $true )
& ( $true
!= ( in @ sK25 @ sK27 ) )
& ( $true
= ( subset @ sK26 @ sK27 ) )
& ( $true
= ( in @ sK25 @ sK26 ) )
& ( powersetI = $true )
& ( notdexE = $true )
& ( exuE2 = $true )
& ( setadjoin__Cong = $true )
& ( dsetconstrER = $true )
& ( subPowSU = $true )
& ( setunion__Cong = $true )
& ( emptysetimpfalse = $true )
& ( subsetI2 = $true )
& ( replAx = $true )
& ( powersetE = $true )
& ( subsetI1 = $true )
& ( quantDeMorgan2 = $true )
& ( singletonsswitch = $true )
& ( omega__Cong = $true )
& ( descr__Cong = $true )
& ( emptyinPowerset = $true )
& ( setextAx = $true )
& ( inCongP = $true )
& ( quantDeMorgan4 = $true )
& ( setext = $true )
& ( exuE1 = $true )
& ( setunionE = $true )
& ( eqimpsubset1 = $true )
& ( setoftrueEq = $true )
& ( upairsetIL = $true )
& ( upairsetIR = $true )
& ( omegaSAx = $true )
& ( emptyInPowerset = $true )
& ( setadjoinE = $true )
& ( exuI2 = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK25,sK26,sK27])],[f308,f400]) ).
thf(f400,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X0 @ X2 ) )
& ( $true
= ( subset @ X1 @ X2 ) )
& ( $true
= ( in @ X0 @ X1 ) ) )
=> ( ( $true
!= ( in @ sK25 @ sK27 ) )
& ( $true
= ( subset @ sK26 @ sK27 ) )
& ( $true
= ( in @ sK25 @ sK26 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f308,plain,
( ( setadjoinAx = $true )
& ( exu__Cong = $true )
& ( setunionI = $true )
& ( nonemptyI = $true )
& ( prop2set2propI = $true )
& ( setbeta = $true )
& ( exuE3u = $true )
& ( powerset__Cong = $true )
& ( upairsetE = $true )
& ( exuEu = $true )
& ( prop2setI = $true )
& ( exuI1 = $true )
& ( emptyinunitempty = $true )
& ( quantDeMorgan3 = $true )
& ( nonemptyE1 = $true )
& ( nonemptyI1 = $true )
& ( setadjoinIR = $true )
& ( exuE3e = $true )
& ( notinsingleton = $true )
& ( setunionAx = $true )
& ( emptysetsubset = $true )
& ( nonemptyImpWitness = $true )
& ( prop2setE = $true )
& ( setadjoinOr = $true )
& ( omegaIndAx = $true )
& ( powersetAx = $true )
& ( dsetconstr__Cong = $true )
& ( vacuousDall = $true )
& ( eqinunit = $true )
& ( quantDeMorgan1 = $true )
& ( emptyE1 = $true )
& ( notdallE = $true )
& ( emptyI = $true )
& ( notinemptyset = $true )
& ( wellorderingAx = $true )
& ( dsetconstrEL = $true )
& ( in__Cong = $true )
& ( descrp = $true )
& ( foundationAx = $true )
& ( emptysetE = $true )
& ( dsetconstrI = $true )
& ( omega0Ax = $true )
& ( noeltsimpempty = $true )
& ( uniqinunit = $true )
& ( emptysetAx = $true )
& ( emptyset__Cong = $true )
& ( setadjoinIL = $true )
& ( exuI3 = $true )
& ( subsetE = $true )
& ( eqimpsubset2 = $true )
& ? [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X0 @ X2 ) )
& ( $true
= ( subset @ X1 @ X2 ) )
& ( $true
= ( in @ X0 @ X1 ) ) )
& ( powersetI = $true )
& ( notdexE = $true )
& ( exuE2 = $true )
& ( setadjoin__Cong = $true )
& ( dsetconstrER = $true )
& ( subPowSU = $true )
& ( setunion__Cong = $true )
& ( emptysetimpfalse = $true )
& ( subsetI2 = $true )
& ( replAx = $true )
& ( powersetE = $true )
& ( subsetI1 = $true )
& ( quantDeMorgan2 = $true )
& ( singletonsswitch = $true )
& ( omega__Cong = $true )
& ( descr__Cong = $true )
& ( emptyinPowerset = $true )
& ( setextAx = $true )
& ( inCongP = $true )
& ( quantDeMorgan4 = $true )
& ( setext = $true )
& ( exuE1 = $true )
& ( setunionE = $true )
& ( eqimpsubset1 = $true )
& ( setoftrueEq = $true )
& ( upairsetIL = $true )
& ( upairsetIR = $true )
& ( omegaSAx = $true )
& ( emptyInPowerset = $true )
& ( setadjoinE = $true )
& ( exuI2 = $true ) ),
inference(flattening,[status(thm)],[f307]) ).
thf(f307,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X0 @ X1 ) )
& ( $true
!= ( in @ X0 @ X2 ) )
& ( $true
= ( subset @ X1 @ X2 ) ) )
& ( subsetE = $true )
& ( emptysetsubset = $true )
& ( subsetI2 = $true )
& ( eqimpsubset1 = $true )
& ( eqimpsubset2 = $true )
& ( subsetI1 = $true )
& ( dsetconstr__Cong = $true )
& ( descr__Cong = $true )
& ( exuEu = $true )
& ( omega__Cong = $true )
& ( setunion__Cong = $true )
& ( powerset__Cong = $true )
& ( setadjoin__Cong = $true )
& ( emptyset__Cong = $true )
& ( exu__Cong = $true )
& ( exuE3u = $true )
& ( in__Cong = $true )
& ( inCongP = $true )
& ( exuI2 = $true )
& ( exuI3 = $true )
& ( exuI1 = $true )
& ( notdallE = $true )
& ( notdexE = $true )
& ( prop2set2propI = $true )
& ( prop2setI = $true )
& ( quantDeMorgan4 = $true )
& ( quantDeMorgan3 = $true )
& ( quantDeMorgan2 = $true )
& ( quantDeMorgan1 = $true )
& ( vacuousDall = $true )
& ( emptyE1 = $true )
& ( upairsetIR = $true )
& ( upairsetIL = $true )
& ( upairsetE = $true )
& ( singletonsswitch = $true )
& ( eqinunit = $true )
& ( notinsingleton = $true )
& ( uniqinunit = $true )
& ( nonemptyImpWitness = $true )
& ( exuE2 = $true )
& ( subPowSU = $true )
& ( setunionE = $true )
& ( setunionI = $true )
& ( powersetE = $true )
& ( emptyInPowerset = $true )
& ( emptyinPowerset = $true )
& ( powersetI = $true )
& ( setoftrueEq = $true )
& ( setadjoinOr = $true )
& ( setadjoinE = $true )
& ( setadjoinIR = $true )
& ( emptyinunitempty = $true )
& ( setadjoinIL = $true )
& ( nonemptyI1 = $true )
& ( nonemptyI = $true )
& ( nonemptyE1 = $true )
& ( setbeta = $true )
& ( noeltsimpempty = $true )
& ( emptyI = $true )
& ( setext = $true )
& ( exuE3e = $true )
& ( notinemptyset = $true )
& ( emptysetimpfalse = $true )
& ( emptysetE = $true )
& ( prop2setE = $true )
& ( exuE1 = $true )
& ( dsetconstrER = $true )
& ( dsetconstrEL = $true )
& ( dsetconstrI = $true )
& ( descrp = $true )
& ( wellorderingAx = $true )
& ( foundationAx = $true )
& ( replAx = $true )
& ( omegaIndAx = $true )
& ( omegaSAx = $true )
& ( omega0Ax = $true )
& ( setunionAx = $true )
& ( powersetAx = $true )
& ( setadjoinAx = $true )
& ( emptysetAx = $true )
& ( setextAx = $true ) ),
inference(ennf_transformation,[status(thm)],[f268]) ).
thf(f268,plain,
~ ( ( setextAx = $true )
=> ( ( emptysetAx = $true )
=> ( ( setadjoinAx = $true )
=> ( ( powersetAx = $true )
=> ( ( setunionAx = $true )
=> ( ( omega0Ax = $true )
=> ( ( omegaSAx = $true )
=> ( ( omegaIndAx = $true )
=> ( ( replAx = $true )
=> ( ( foundationAx = $true )
=> ( ( wellorderingAx = $true )
=> ( ( descrp = $true )
=> ( ( dsetconstrI = $true )
=> ( ( dsetconstrEL = $true )
=> ( ( dsetconstrER = $true )
=> ( ( exuE1 = $true )
=> ( ( prop2setE = $true )
=> ( ( emptysetE = $true )
=> ( ( emptysetimpfalse = $true )
=> ( ( notinemptyset = $true )
=> ( ( exuE3e = $true )
=> ( ( setext = $true )
=> ( ( emptyI = $true )
=> ( ( noeltsimpempty = $true )
=> ( ( setbeta = $true )
=> ( ( nonemptyE1 = $true )
=> ( ( nonemptyI = $true )
=> ( ( nonemptyI1 = $true )
=> ( ( setadjoinIL = $true )
=> ( ( emptyinunitempty = $true )
=> ( ( setadjoinIR = $true )
=> ( ( setadjoinE = $true )
=> ( ( setadjoinOr = $true )
=> ( ( setoftrueEq = $true )
=> ( ( powersetI = $true )
=> ( ( emptyinPowerset = $true )
=> ( ( emptyInPowerset = $true )
=> ( ( powersetE = $true )
=> ( ( setunionI = $true )
=> ( ( setunionE = $true )
=> ( ( subPowSU = $true )
=> ( ( exuE2 = $true )
=> ( ( nonemptyImpWitness = $true )
=> ( ( uniqinunit = $true )
=> ( ( notinsingleton = $true )
=> ( ( eqinunit = $true )
=> ( ( singletonsswitch = $true )
=> ( ( upairsetE = $true )
=> ( ( upairsetIL = $true )
=> ( ( upairsetIR = $true )
=> ( ( emptyE1 = $true )
=> ( ( vacuousDall = $true )
=> ( ( quantDeMorgan1 = $true )
=> ( ( quantDeMorgan2 = $true )
=> ( ( quantDeMorgan3 = $true )
=> ( ( quantDeMorgan4 = $true )
=> ( ( prop2setI = $true )
=> ( ( prop2set2propI = $true )
=> ( ( notdexE = $true )
=> ( ( notdallE = $true )
=> ( ( exuI1 = $true )
=> ( ( exuI3 = $true )
=> ( ( exuI2 = $true )
=> ( ( inCongP = $true )
=> ( ( in__Cong = $true )
=> ( ( exuE3u = $true )
=> ( ( exu__Cong = $true )
=> ( ( emptyset__Cong = $true )
=> ( ( setadjoin__Cong = $true )
=> ( ( powerset__Cong = $true )
=> ( ( setunion__Cong = $true )
=> ( ( omega__Cong = $true )
=> ( ( exuEu = $true )
=> ( ( descr__Cong = $true )
=> ( ( dsetconstr__Cong = $true )
=> ( ( subsetI1 = $true )
=> ( ( eqimpsubset2 = $true )
=> ( ( eqimpsubset1 = $true )
=> ( ( subsetI2 = $true )
=> ( ( emptysetsubset = $true )
=> ( ( subsetE = $true )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( subset @ X1 @ X2 ) )
=> ( ( $true
!= ( in @ X0 @ X2 ) )
=> ( $true
!= ( in @ X0 @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(flattening,[status(thm)],[f233]) ).
thf(f233,plain,
~ ( ( setextAx = $true )
=> ( ( emptysetAx = $true )
=> ( ( setadjoinAx = $true )
=> ( ( powersetAx = $true )
=> ( ( setunionAx = $true )
=> ( ( omega0Ax = $true )
=> ( ( omegaSAx = $true )
=> ( ( omegaIndAx = $true )
=> ( ( replAx = $true )
=> ( ( foundationAx = $true )
=> ( ( wellorderingAx = $true )
=> ( ( descrp = $true )
=> ( ( dsetconstrI = $true )
=> ( ( dsetconstrEL = $true )
=> ( ( dsetconstrER = $true )
=> ( ( exuE1 = $true )
=> ( ( prop2setE = $true )
=> ( ( emptysetE = $true )
=> ( ( emptysetimpfalse = $true )
=> ( ( notinemptyset = $true )
=> ( ( exuE3e = $true )
=> ( ( setext = $true )
=> ( ( emptyI = $true )
=> ( ( noeltsimpempty = $true )
=> ( ( setbeta = $true )
=> ( ( nonemptyE1 = $true )
=> ( ( nonemptyI = $true )
=> ( ( nonemptyI1 = $true )
=> ( ( setadjoinIL = $true )
=> ( ( emptyinunitempty = $true )
=> ( ( setadjoinIR = $true )
=> ( ( setadjoinE = $true )
=> ( ( setadjoinOr = $true )
=> ( ( setoftrueEq = $true )
=> ( ( powersetI = $true )
=> ( ( emptyinPowerset = $true )
=> ( ( emptyInPowerset = $true )
=> ( ( powersetE = $true )
=> ( ( setunionI = $true )
=> ( ( setunionE = $true )
=> ( ( subPowSU = $true )
=> ( ( exuE2 = $true )
=> ( ( nonemptyImpWitness = $true )
=> ( ( uniqinunit = $true )
=> ( ( notinsingleton = $true )
=> ( ( eqinunit = $true )
=> ( ( singletonsswitch = $true )
=> ( ( upairsetE = $true )
=> ( ( upairsetIL = $true )
=> ( ( upairsetIR = $true )
=> ( ( emptyE1 = $true )
=> ( ( vacuousDall = $true )
=> ( ( quantDeMorgan1 = $true )
=> ( ( quantDeMorgan2 = $true )
=> ( ( quantDeMorgan3 = $true )
=> ( ( quantDeMorgan4 = $true )
=> ( ( prop2setI = $true )
=> ( ( prop2set2propI = $true )
=> ( ( notdexE = $true )
=> ( ( notdallE = $true )
=> ( ( exuI1 = $true )
=> ( ( exuI3 = $true )
=> ( ( exuI2 = $true )
=> ( ( inCongP = $true )
=> ( ( in__Cong = $true )
=> ( ( exuE3u = $true )
=> ( ( exu__Cong = $true )
=> ( ( emptyset__Cong = $true )
=> ( ( setadjoin__Cong = $true )
=> ( ( powerset__Cong = $true )
=> ( ( setunion__Cong = $true )
=> ( ( omega__Cong = $true )
=> ( ( exuEu = $true )
=> ( ( descr__Cong = $true )
=> ( ( dsetconstr__Cong = $true )
=> ( ( subsetI1 = $true )
=> ( ( eqimpsubset2 = $true )
=> ( ( eqimpsubset1 = $true )
=> ( ( subsetI2 = $true )
=> ( ( emptysetsubset = $true )
=> ( ( subsetE = $true )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( subset @ X1 @ X2 ) )
=> ( ( $true
!= ( in @ X0 @ X2 ) )
=> ( $true
!= ( in @ X0 @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f232]) ).
thf(f232,plain,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ! [X0: $i,X1: $i,X2: $i] :
( ( subset @ X1 @ X2 )
=> ( ~ ( in @ X0 @ X2 )
=> ~ ( in @ X0 @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f85]) ).
thf(f85,negated_conjecture,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ! [X1: $i,X3: $i,X4: $i] :
( ( subset @ X3 @ X4 )
=> ( ~ ( in @ X1 @ X4 )
=> ~ ( in @ X1 @ X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f84]) ).
thf(f84,conjecture,
( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ! [X1: $i,X3: $i,X4: $i] :
( ( subset @ X3 @ X4 )
=> ( ~ ( in @ X1 @ X4 )
=> ~ ( in @ X1 @ X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.cd1eMribCG/DTF2THF_26070.p',subsetE2) ).
thf(f1302,plain,
( $true
!= ( in @ sK25 @ sK26 ) ),
inference(trivial_inequality_removal,[status(thm)],[f1296]) ).
thf(f1296,plain,
( ( $true
!= ( in @ sK25 @ sK26 ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f1295,f836]) ).
thf(f836,plain,
( $true
= ( subset @ sK26 @ sK27 ) ),
inference(cnf_transformation,[status(thm)],[f401]) ).
thf(f1295,plain,
! [X0: $i] :
( ( $true
!= ( subset @ X0 @ sK27 ) )
| ( $true
!= ( in @ sK25 @ X0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f1294]) ).
thf(f1294,plain,
! [X0: $i] :
( ( $true
!= ( subset @ X0 @ sK27 ) )
| ( $true
!= ( in @ sK25 @ X0 ) )
| ( $true != $true ) ),
inference(forward_demodulation,[status(thm)],[f1293,f839]) ).
thf(f839,plain,
subsetE = $true,
inference(cnf_transformation,[status(thm)],[f401]) ).
thf(f1293,plain,
! [X0: $i] :
( ( $true
!= ( in @ sK25 @ X0 ) )
| ( $true
!= ( subset @ X0 @ sK27 ) )
| ( subsetE != $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f1290]) ).
thf(f1290,plain,
! [X0: $i] :
( ( $true
!= ( subset @ X0 @ sK27 ) )
| ( subsetE != $true )
| ( $true
!= ( in @ sK25 @ X0 ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f837,f1035]) ).
thf(f1035,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X3 @ X4 )
= $true )
| ( $true
!= ( in @ X3 @ X5 ) )
| ( subsetE != $true )
| ( $true
!= ( subset @ X5 @ X4 ) ) ),
inference(cnf_transformation,[status(thm)],[f585]) ).
thf(f585,plain,
( ( ( subsetE = $true )
| ( ( $true
= ( in @ sK125 @ sK127 ) )
& ( $true
!= ( in @ sK125 @ sK126 ) )
& ( $true
= ( subset @ sK127 @ sK126 ) ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X3 @ X5 ) )
| ( ( in @ X3 @ X4 )
= $true )
| ( $true
!= ( subset @ X5 @ X4 ) ) )
| ( subsetE != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK125,sK126,sK127])],[f583,f584]) ).
thf(f584,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X0 @ X2 ) )
& ( $true
!= ( in @ X0 @ X1 ) )
& ( ( subset @ X2 @ X1 )
= $true ) )
=> ( ( $true
= ( in @ sK125 @ sK127 ) )
& ( $true
!= ( in @ sK125 @ sK126 ) )
& ( $true
= ( subset @ sK127 @ sK126 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f583,plain,
( ( ( subsetE = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X0 @ X2 ) )
& ( $true
!= ( in @ X0 @ X1 ) )
& ( ( subset @ X2 @ X1 )
= $true ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X3 @ X5 ) )
| ( ( in @ X3 @ X4 )
= $true )
| ( $true
!= ( subset @ X5 @ X4 ) ) )
| ( subsetE != $true ) ) ),
inference(rectify,[status(thm)],[f582]) ).
thf(f582,plain,
( ( ( subsetE = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X0 @ X2 ) )
& ( $true
!= ( in @ X0 @ X1 ) )
& ( ( subset @ X2 @ X1 )
= $true ) ) )
& ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X0 @ X2 ) )
| ( $true
= ( in @ X0 @ X1 ) )
| ( ( subset @ X2 @ X1 )
!= $true ) )
| ( subsetE != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f284]) ).
thf(f284,plain,
( ( subsetE = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X0 @ X2 ) )
| ( $true
= ( in @ X0 @ X1 ) )
| ( ( subset @ X2 @ X1 )
!= $true ) ) ),
inference(flattening,[status(thm)],[f283]) ).
thf(f283,plain,
( ( subsetE = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X0 @ X1 ) )
| ( $true
!= ( in @ X0 @ X2 ) )
| ( ( subset @ X2 @ X1 )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f179]) ).
thf(f179,plain,
( ( subsetE = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X2 @ X1 )
= $true )
=> ( ( $true
= ( in @ X0 @ X2 ) )
=> ( $true
= ( in @ X0 @ X1 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f178]) ).
thf(f178,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X2 @ X1 )
=> ( ( in @ X0 @ X2 )
=> ( in @ X0 @ X1 ) ) )
= subsetE ),
inference(rectify,[status(thm)],[f83]) ).
thf(f83,axiom,
! [X1: $i,X4: $i,X3: $i] :
( ( ( subset @ X3 @ X4 )
=> ( ( in @ X1 @ X3 )
=> ( in @ X1 @ X4 ) ) )
= subsetE ),
file('/export/starexec/sandbox2/tmp/tmp.cd1eMribCG/DTF2THF_26070.p',subsetE) ).
thf(f837,plain,
( $true
!= ( in @ sK25 @ sK27 ) ),
inference(cnf_transformation,[status(thm)],[f401]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU565^1 : TPTP v9.2.1. Released v3.7.0.
% 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n006.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 12:27:00 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.28/0.46 ---- Original DTF file ---
% 0.28/0.46 thf(spec,logic,$$dhol).
% 0.28/0.46 %------------------------------------------------------------------------------
% 0.28/0.46 % File : SEU565^1 : TPTP v9.2.1. Released v3.7.0.
% 0.28/0.46 % Domain : Set Theory
% 0.28/0.46 % Problem : Preliminary Notions - Relations on Sets - Subsets
% 0.28/0.46 % Version : Especial.
% 0.28/0.46 % English : (! A:i.! B:i.! x:i.subset A B -> ~(in x B) -> ~(in x A))
% 0.28/0.46
% 0.28/0.46 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.28/0.46 % Source : [Bro08]
% 0.28/0.46 % Names : ZFC067g [Bro08]
% 0.28/0.46
% 0.28/0.46 % Status : Theorem
% 0.28/0.46 % Rating : 0.11 v9.1.0, 0.25 v9.0.0, 0.30 v8.2.0, 0.23 v8.1.0, 0.00 v7.4.0, 0.11 v7.2.0, 0.00 v7.1.0, 0.25 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.14 v6.1.0, 0.29 v5.5.0, 0.33 v5.4.0, 0.40 v5.1.0, 0.60 v5.0.0, 0.40 v4.1.0, 0.67 v4.0.1, 1.00 v3.7.0
% 0.28/0.46 % Syntax : Number of formulae : 180 ( 83 unt; 96 typ; 83 def)
% 0.28/0.46 % Number of atoms : 456 ( 128 equ; 0 cnn)
% 0.28/0.46 % Maximal formula atoms : 84 ( 5 avg)
% 0.28/0.46 % Number of connectives : 729 ( 23 ~; 5 |; 27 &; 450 @)
% 0.28/0.46 % ( 14 <=>; 210 =>; 0 <=; 0 <~>)
% 0.28/0.46 % Maximal formula depth : 90 ( 2 avg)
% 0.28/0.46 % Number of types : 2 ( 0 usr)
% 0.28/0.46 % Number of type conns : 53 ( 53 >; 0 *; 0 +; 0 <<)
% 0.28/0.46 % Number of symbols : 99 ( 96 usr; 85 con; 0-2 aty)
% 0.28/0.46 % Number of variables : 259 ( 28 ^; 203 !; 28 ?; 259 :)
% 0.28/0.46 % SPC : TH0_THM_EQU_NAR
% 0.28/0.46
% 0.28/0.46 % Comments : http://mathgate.info/detsetitem.php?id=474
% 0.28/0.46 %------------------------------------------------------------------------------
% 0.28/0.46 thf(in_type,type,
% 0.28/0.46 in: $i > $i > $o ).
% 0.28/0.46
% 0.28/0.46 thf(exu_type,type,
% 0.28/0.46 exu: ( $i > $o ) > $o ).
% 0.28/0.46
% 0.28/0.46 thf(exu,definition,
% 0.28/0.46 ( exu
% 0.28/0.46 = ( ^ [Xphi: $i > $o] :
% 0.28/0.46 ? [Xx: $i] :
% 0.28/0.46 ( ( Xphi @ Xx )
% 0.28/0.46 & ! [Xy: $i] :
% 0.28/0.46 ( ( Xphi @ Xy )
% 0.28/0.46 => ( Xx = Xy ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(setextAx_type,type,
% 0.28/0.46 setextAx: $o ).
% 0.28/0.46
% 0.28/0.46 thf(setextAx,definition,
% 0.28/0.46 ( setextAx
% 0.28/0.46 = ( ! [A: $i,B: $i] :
% 0.28/0.46 ( ! [Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ A )
% 0.28/0.46 <=> ( in @ Xx @ B ) )
% 0.28/0.46 => ( A = B ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(emptyset_type,type,
% 0.28/0.46 emptyset: $i ).
% 0.28/0.46
% 0.28/0.46 thf(emptysetAx_type,type,
% 0.28/0.46 emptysetAx: $o ).
% 0.28/0.46
% 0.28/0.46 thf(emptysetAx,definition,
% 0.28/0.46 ( emptysetAx
% 0.28/0.46 = ( ! [Xx: $i] :
% 0.28/0.46 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(setadjoin_type,type,
% 0.28/0.46 setadjoin: $i > $i > $i ).
% 0.28/0.46
% 0.28/0.46 thf(setadjoinAx_type,type,
% 0.28/0.46 setadjoinAx: $o ).
% 0.28/0.46
% 0.28/0.46 thf(setadjoinAx,definition,
% 0.28/0.46 ( setadjoinAx
% 0.28/0.46 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.28/0.46 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.28/0.46 <=> ( ( Xy = Xx )
% 0.28/0.46 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(powerset_type,type,
% 0.28/0.46 powerset: $i > $i ).
% 0.28/0.46
% 0.28/0.46 thf(powersetAx_type,type,
% 0.28/0.46 powersetAx: $o ).
% 0.28/0.46
% 0.28/0.46 thf(powersetAx,definition,
% 0.28/0.46 ( powersetAx
% 0.28/0.46 = ( ! [A: $i,B: $i] :
% 0.28/0.46 ( ( in @ B @ ( powerset @ A ) )
% 0.28/0.46 <=> ! [Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ B )
% 0.28/0.46 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(setunion_type,type,
% 0.28/0.46 setunion: $i > $i ).
% 0.28/0.46
% 0.28/0.46 thf(setunionAx_type,type,
% 0.28/0.46 setunionAx: $o ).
% 0.28/0.46
% 0.28/0.46 thf(setunionAx,definition,
% 0.28/0.46 ( setunionAx
% 0.28/0.46 = ( ! [A: $i,Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ ( setunion @ A ) )
% 0.28/0.46 <=> ? [B: $i] :
% 0.28/0.46 ( ( in @ Xx @ B )
% 0.28/0.46 & ( in @ B @ A ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(omega_type,type,
% 0.28/0.46 omega: $i ).
% 0.28/0.46
% 0.28/0.46 thf(omega0Ax_type,type,
% 0.28/0.46 omega0Ax: $o ).
% 0.28/0.46
% 0.28/0.46 thf(omega0Ax,definition,
% 0.28/0.46 ( omega0Ax
% 0.28/0.46 = ( in @ emptyset @ omega ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(omegaSAx_type,type,
% 0.28/0.46 omegaSAx: $o ).
% 0.28/0.46
% 0.28/0.46 thf(omegaSAx,definition,
% 0.28/0.46 ( omegaSAx
% 0.28/0.46 = ( ! [Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ omega )
% 0.28/0.46 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(omegaIndAx_type,type,
% 0.28/0.46 omegaIndAx: $o ).
% 0.28/0.46
% 0.28/0.46 thf(omegaIndAx,definition,
% 0.28/0.46 ( omegaIndAx
% 0.28/0.46 = ( ! [A: $i] :
% 0.28/0.46 ( ( ( in @ emptyset @ A )
% 0.28/0.46 & ! [Xx: $i] :
% 0.28/0.46 ( ( ( in @ Xx @ omega )
% 0.28/0.46 & ( in @ Xx @ A ) )
% 0.28/0.46 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 0.28/0.46 => ! [Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ omega )
% 0.28/0.46 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(replAx_type,type,
% 0.28/0.46 replAx: $o ).
% 0.28/0.46
% 0.28/0.46 thf(replAx,definition,
% 0.28/0.46 ( replAx
% 0.28/0.46 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 0.28/0.46 ( ! [Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ A )
% 0.28/0.46 => ( exu
% 0.28/0.46 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 0.28/0.46 => ? [B: $i] :
% 0.28/0.46 ! [Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ B )
% 0.28/0.46 <=> ? [Xy: $i] :
% 0.28/0.46 ( ( in @ Xy @ A )
% 0.28/0.46 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(foundationAx_type,type,
% 0.28/0.46 foundationAx: $o ).
% 0.28/0.46
% 0.28/0.46 thf(foundationAx,definition,
% 0.28/0.46 ( foundationAx
% 0.28/0.46 = ( ! [A: $i] :
% 0.28/0.46 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.28/0.46 => ? [B: $i] :
% 0.28/0.46 ( ( in @ B @ A )
% 0.28/0.46 & ~ ? [Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ B )
% 0.28/0.46 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(wellorderingAx_type,type,
% 0.28/0.46 wellorderingAx: $o ).
% 0.28/0.46
% 0.28/0.46 thf(wellorderingAx,definition,
% 0.28/0.46 ( wellorderingAx
% 0.28/0.46 = ( ! [A: $i] :
% 0.28/0.46 ? [B: $i] :
% 0.28/0.46 ( ! [C: $i] :
% 0.28/0.46 ( ( in @ C @ B )
% 0.28/0.46 => ! [Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ C )
% 0.28/0.46 => ( in @ Xx @ A ) ) )
% 0.28/0.46 & ! [Xx: $i,Xy: $i] :
% 0.28/0.46 ( ( ( in @ Xx @ A )
% 0.28/0.46 & ( in @ Xy @ A ) )
% 0.28/0.46 => ( ! [C: $i] :
% 0.28/0.46 ( ( in @ C @ B )
% 0.28/0.46 => ( ( in @ Xx @ C )
% 0.28/0.46 <=> ( in @ Xy @ C ) ) )
% 0.28/0.46 => ( Xx = Xy ) ) )
% 0.28/0.46 & ! [C: $i,D: $i] :
% 0.28/0.46 ( ( ( in @ C @ B )
% 0.28/0.46 & ( in @ D @ B ) )
% 0.28/0.46 => ( ! [Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ C )
% 0.28/0.46 => ( in @ Xx @ D ) )
% 0.28/0.46 | ! [Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ D )
% 0.28/0.46 => ( in @ Xx @ C ) ) ) )
% 0.28/0.46 & ! [C: $i] :
% 0.28/0.46 ( ( ! [Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ C )
% 0.28/0.46 => ( in @ Xx @ A ) )
% 0.28/0.46 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 0.28/0.46 => ? [D: $i,Xx: $i] :
% 0.28/0.46 ( ( in @ D @ B )
% 0.28/0.46 & ( in @ Xx @ C )
% 0.28/0.46 & ~ ? [Xy: $i] :
% 0.28/0.46 ( ( in @ Xy @ D )
% 0.28/0.46 & ( in @ Xy @ C ) )
% 0.28/0.46 & ! [E: $i] :
% 0.28/0.46 ( ( in @ E @ B )
% 0.28/0.46 => ( ! [Xy: $i] :
% 0.28/0.46 ( ( in @ Xy @ E )
% 0.28/0.46 => ( in @ Xy @ D ) )
% 0.28/0.46 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(descr_type,type,
% 0.28/0.46 descr: ( $i > $o ) > $i ).
% 0.28/0.46
% 0.28/0.46 thf(descrp_type,type,
% 0.28/0.46 descrp: $o ).
% 0.28/0.46
% 0.28/0.46 thf(descrp,definition,
% 0.28/0.46 ( descrp
% 0.28/0.46 = ( ! [Xphi: $i > $o] :
% 0.28/0.46 ( ( exu
% 0.28/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.46 => ( Xphi
% 0.28/0.46 @ ( descr
% 0.28/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(dsetconstr_type,type,
% 0.28/0.46 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.28/0.46
% 0.28/0.46 thf(dsetconstrI_type,type,
% 0.28/0.46 dsetconstrI: $o ).
% 0.28/0.46
% 0.28/0.46 thf(dsetconstrI,definition,
% 0.28/0.46 ( dsetconstrI
% 0.28/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ A )
% 0.28/0.46 => ( ( Xphi @ Xx )
% 0.28/0.46 => ( in @ Xx
% 0.28/0.46 @ ( dsetconstr @ A
% 0.28/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(dsetconstrEL_type,type,
% 0.28/0.46 dsetconstrEL: $o ).
% 0.28/0.46
% 0.28/0.46 thf(dsetconstrEL,definition,
% 0.28/0.46 ( dsetconstrEL
% 0.28/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.28/0.46 ( ( in @ Xx
% 0.28/0.46 @ ( dsetconstr @ A
% 0.28/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.28/0.46 => ( in @ Xx @ A ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(dsetconstrER_type,type,
% 0.28/0.46 dsetconstrER: $o ).
% 0.28/0.46
% 0.28/0.46 thf(dsetconstrER,definition,
% 0.28/0.46 ( dsetconstrER
% 0.28/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.28/0.46 ( ( in @ Xx
% 0.28/0.46 @ ( dsetconstr @ A
% 0.28/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.28/0.46 => ( Xphi @ Xx ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(exuE1_type,type,
% 0.28/0.46 exuE1: $o ).
% 0.28/0.46
% 0.28/0.46 thf(exuE1,definition,
% 0.28/0.46 ( exuE1
% 0.28/0.46 = ( ! [Xphi: $i > $o] :
% 0.28/0.46 ( ( exu
% 0.28/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.46 => ? [Xx: $i] :
% 0.28/0.46 ( ( Xphi @ Xx )
% 0.28/0.46 & ! [Xy: $i] :
% 0.28/0.46 ( ( Xphi @ Xy )
% 0.28/0.46 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(prop2set_type,type,
% 0.28/0.46 prop2set: $o > $i ).
% 0.28/0.46
% 0.28/0.46 thf(prop2setE_type,type,
% 0.28/0.46 prop2setE: $o ).
% 0.28/0.46
% 0.28/0.46 thf(prop2setE,definition,
% 0.28/0.46 ( prop2setE
% 0.28/0.46 = ( ! [Xphi: $o,Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 0.28/0.46 => Xphi ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(emptysetE_type,type,
% 0.28/0.46 emptysetE: $o ).
% 0.28/0.46
% 0.28/0.46 thf(emptysetE,definition,
% 0.28/0.46 ( emptysetE
% 0.28/0.46 = ( ! [Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ emptyset )
% 0.28/0.46 => ! [Xphi: $o] : Xphi ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(emptysetimpfalse_type,type,
% 0.28/0.46 emptysetimpfalse: $o ).
% 0.28/0.46
% 0.28/0.46 thf(emptysetimpfalse,definition,
% 0.28/0.46 ( emptysetimpfalse
% 0.28/0.46 = ( ! [Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ emptyset )
% 0.28/0.46 => $false ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(notinemptyset_type,type,
% 0.28/0.46 notinemptyset: $o ).
% 0.28/0.46
% 0.28/0.46 thf(notinemptyset,definition,
% 0.28/0.46 ( notinemptyset
% 0.28/0.46 = ( ! [Xx: $i] :
% 0.28/0.46 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(exuE3e_type,type,
% 0.28/0.46 exuE3e: $o ).
% 0.28/0.46
% 0.28/0.46 thf(exuE3e,definition,
% 0.28/0.46 ( exuE3e
% 0.28/0.46 = ( ! [Xphi: $i > $o] :
% 0.28/0.46 ( ( exu
% 0.28/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.46 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(setext_type,type,
% 0.28/0.46 setext: $o ).
% 0.28/0.46
% 0.28/0.46 thf(setext,definition,
% 0.28/0.46 ( setext
% 0.28/0.46 = ( ! [A: $i,B: $i] :
% 0.28/0.46 ( ! [Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ A )
% 0.28/0.46 => ( in @ Xx @ B ) )
% 0.28/0.46 => ( ! [Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ B )
% 0.28/0.46 => ( in @ Xx @ A ) )
% 0.28/0.46 => ( A = B ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(emptyI_type,type,
% 0.28/0.46 emptyI: $o ).
% 0.28/0.46
% 0.28/0.46 thf(emptyI,definition,
% 0.28/0.46 ( emptyI
% 0.28/0.46 = ( ! [A: $i] :
% 0.28/0.46 ( ! [Xx: $i] :
% 0.28/0.46 ~ ( in @ Xx @ A )
% 0.28/0.46 => ( A = emptyset ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(noeltsimpempty_type,type,
% 0.28/0.46 noeltsimpempty: $o ).
% 0.28/0.46
% 0.28/0.46 thf(noeltsimpempty,definition,
% 0.28/0.46 ( noeltsimpempty
% 0.28/0.46 = ( ! [A: $i] :
% 0.28/0.46 ( ! [Xx: $i] :
% 0.28/0.46 ~ ( in @ Xx @ A )
% 0.28/0.46 => ( A = emptyset ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(setbeta_type,type,
% 0.28/0.46 setbeta: $o ).
% 0.28/0.46
% 0.28/0.46 thf(setbeta,definition,
% 0.28/0.46 ( setbeta
% 0.28/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ A )
% 0.28/0.46 => ( ( in @ Xx
% 0.28/0.46 @ ( dsetconstr @ A
% 0.28/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.28/0.46 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(nonempty_type,type,
% 0.28/0.46 nonempty: $i > $o ).
% 0.28/0.46
% 0.28/0.46 thf(nonempty,definition,
% 0.28/0.46 ( nonempty
% 0.28/0.46 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(nonemptyE1_type,type,
% 0.28/0.46 nonemptyE1: $o ).
% 0.28/0.46
% 0.28/0.46 thf(nonemptyE1,definition,
% 0.28/0.46 ( nonemptyE1
% 0.28/0.46 = ( ! [A: $i] :
% 0.28/0.46 ( ( nonempty @ A )
% 0.28/0.46 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(nonemptyI_type,type,
% 0.28/0.46 nonemptyI: $o ).
% 0.28/0.46
% 0.28/0.46 thf(nonemptyI,definition,
% 0.28/0.46 ( nonemptyI
% 0.28/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ A )
% 0.28/0.46 => ( ( Xphi @ Xx )
% 0.28/0.46 => ( nonempty
% 0.28/0.46 @ ( dsetconstr @ A
% 0.28/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(nonemptyI1_type,type,
% 0.28/0.46 nonemptyI1: $o ).
% 0.28/0.46
% 0.28/0.46 thf(nonemptyI1,definition,
% 0.28/0.46 ( nonemptyI1
% 0.28/0.46 = ( ! [A: $i] :
% 0.28/0.46 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.28/0.46 => ( nonempty @ A ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(setadjoinIL_type,type,
% 0.28/0.46 setadjoinIL: $o ).
% 0.28/0.46
% 0.28/0.46 thf(setadjoinIL,definition,
% 0.28/0.46 ( setadjoinIL
% 0.28/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(emptyinunitempty_type,type,
% 0.28/0.46 emptyinunitempty: $o ).
% 0.28/0.46
% 0.28/0.46 thf(emptyinunitempty,definition,
% 0.28/0.46 ( emptyinunitempty
% 0.28/0.46 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(setadjoinIR_type,type,
% 0.28/0.46 setadjoinIR: $o ).
% 0.28/0.46
% 0.28/0.46 thf(setadjoinIR,definition,
% 0.28/0.46 ( setadjoinIR
% 0.28/0.46 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.28/0.46 ( ( in @ Xy @ A )
% 0.28/0.46 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(setadjoinE_type,type,
% 0.28/0.46 setadjoinE: $o ).
% 0.28/0.46
% 0.28/0.46 thf(setadjoinE,definition,
% 0.28/0.46 ( setadjoinE
% 0.28/0.46 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.28/0.46 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.28/0.46 => ! [Xphi: $o] :
% 0.28/0.46 ( ( ( Xy = Xx )
% 0.28/0.46 => Xphi )
% 0.28/0.46 => ( ( ( in @ Xy @ A )
% 0.28/0.46 => Xphi )
% 0.28/0.46 => Xphi ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(setadjoinOr_type,type,
% 0.28/0.46 setadjoinOr: $o ).
% 0.28/0.46
% 0.28/0.46 thf(setadjoinOr,definition,
% 0.28/0.46 ( setadjoinOr
% 0.28/0.46 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.28/0.46 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.28/0.46 => ( ( Xy = Xx )
% 0.28/0.46 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(setoftrueEq_type,type,
% 0.28/0.46 setoftrueEq: $o ).
% 0.28/0.46
% 0.28/0.46 thf(setoftrueEq,definition,
% 0.28/0.46 ( setoftrueEq
% 0.28/0.46 = ( ! [A: $i] :
% 0.28/0.46 ( ( dsetconstr @ A
% 0.28/0.46 @ ^ [Xx: $i] : $true )
% 0.28/0.46 = A ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(powersetI_type,type,
% 0.28/0.46 powersetI: $o ).
% 0.28/0.46
% 0.28/0.46 thf(powersetI,definition,
% 0.28/0.46 ( powersetI
% 0.28/0.46 = ( ! [A: $i,B: $i] :
% 0.28/0.46 ( ! [Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ B )
% 0.28/0.46 => ( in @ Xx @ A ) )
% 0.28/0.46 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(emptyinPowerset_type,type,
% 0.28/0.46 emptyinPowerset: $o ).
% 0.28/0.46
% 0.28/0.46 thf(emptyinPowerset,definition,
% 0.28/0.46 ( emptyinPowerset
% 0.28/0.46 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(emptyInPowerset_type,type,
% 0.28/0.46 emptyInPowerset: $o ).
% 0.28/0.46
% 0.28/0.46 thf(emptyInPowerset,definition,
% 0.28/0.46 ( emptyInPowerset
% 0.28/0.46 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(powersetE_type,type,
% 0.28/0.46 powersetE: $o ).
% 0.28/0.46
% 0.28/0.46 thf(powersetE,definition,
% 0.28/0.46 ( powersetE
% 0.28/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.46 ( ( in @ B @ ( powerset @ A ) )
% 0.28/0.46 => ( ( in @ Xx @ B )
% 0.28/0.46 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(setunionI_type,type,
% 0.28/0.46 setunionI: $o ).
% 0.28/0.46
% 0.28/0.46 thf(setunionI,definition,
% 0.28/0.46 ( setunionI
% 0.28/0.46 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.28/0.46 ( ( in @ Xx @ B )
% 0.28/0.46 => ( ( in @ B @ A )
% 0.28/0.46 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(setunionE_type,type,
% 0.28/0.46 setunionE: $o ).
% 0.28/0.46
% 0.28/0.46 thf(setunionE,definition,
% 0.28/0.46 ( setunionE
% 0.28/0.46 = ( ! [A: $i,Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ ( setunion @ A ) )
% 0.28/0.46 => ! [Xphi: $o] :
% 0.28/0.46 ( ! [B: $i] :
% 0.28/0.46 ( ( in @ Xx @ B )
% 0.28/0.46 => ( ( in @ B @ A )
% 0.28/0.46 => Xphi ) )
% 0.28/0.46 => Xphi ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(subPowSU_type,type,
% 0.28/0.46 subPowSU: $o ).
% 0.28/0.46
% 0.28/0.46 thf(subPowSU,definition,
% 0.28/0.46 ( subPowSU
% 0.28/0.46 = ( ! [A: $i,Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ A )
% 0.28/0.46 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(exuE2_type,type,
% 0.28/0.46 exuE2: $o ).
% 0.28/0.46
% 0.28/0.46 thf(exuE2,definition,
% 0.28/0.46 ( exuE2
% 0.28/0.46 = ( ! [Xphi: $i > $o] :
% 0.28/0.46 ( ( exu
% 0.28/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.46 => ? [Xx: $i] :
% 0.28/0.46 ! [Xy: $i] :
% 0.28/0.46 ( ( Xphi @ Xy )
% 0.28/0.46 <=> ( Xy = Xx ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(nonemptyImpWitness_type,type,
% 0.28/0.46 nonemptyImpWitness: $o ).
% 0.28/0.46
% 0.28/0.46 thf(nonemptyImpWitness,definition,
% 0.28/0.46 ( nonemptyImpWitness
% 0.28/0.46 = ( ! [A: $i] :
% 0.28/0.46 ( ( nonempty @ A )
% 0.28/0.46 => ? [Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ A )
% 0.28/0.46 & $true ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(uniqinunit_type,type,
% 0.28/0.46 uniqinunit: $o ).
% 0.28/0.46
% 0.28/0.46 thf(uniqinunit,definition,
% 0.28/0.46 ( uniqinunit
% 0.28/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.28/0.46 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.28/0.46 => ( Xx = Xy ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(notinsingleton_type,type,
% 0.28/0.46 notinsingleton: $o ).
% 0.28/0.46
% 0.28/0.46 thf(notinsingleton,definition,
% 0.28/0.46 ( notinsingleton
% 0.28/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.28/0.46 ( ( Xx != Xy )
% 0.28/0.46 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(eqinunit_type,type,
% 0.28/0.46 eqinunit: $o ).
% 0.28/0.46
% 0.28/0.46 thf(eqinunit,definition,
% 0.28/0.46 ( eqinunit
% 0.28/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.28/0.46 ( ( Xx = Xy )
% 0.28/0.46 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(singletonsswitch_type,type,
% 0.28/0.46 singletonsswitch: $o ).
% 0.28/0.46
% 0.28/0.46 thf(singletonsswitch,definition,
% 0.28/0.46 ( singletonsswitch
% 0.28/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.28/0.46 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.28/0.46 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(upairsetE_type,type,
% 0.28/0.46 upairsetE: $o ).
% 0.28/0.46
% 0.28/0.46 thf(upairsetE,definition,
% 0.28/0.46 ( upairsetE
% 0.28/0.46 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.28/0.46 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.28/0.46 => ( ( Xz = Xx )
% 0.28/0.46 | ( Xz = Xy ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(upairsetIL_type,type,
% 0.28/0.46 upairsetIL: $o ).
% 0.28/0.46
% 0.28/0.46 thf(upairsetIL,definition,
% 0.28/0.46 ( upairsetIL
% 0.28/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(upairsetIR_type,type,
% 0.28/0.46 upairsetIR: $o ).
% 0.28/0.46
% 0.28/0.46 thf(upairsetIR,definition,
% 0.28/0.46 ( upairsetIR
% 0.28/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(emptyE1_type,type,
% 0.28/0.46 emptyE1: $o ).
% 0.28/0.46
% 0.28/0.46 thf(emptyE1,definition,
% 0.28/0.46 ( emptyE1
% 0.28/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.28/0.46 ( ? [Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ A )
% 0.28/0.46 & ( Xphi @ Xx ) )
% 0.28/0.46 => ( ( ( dsetconstr @ A
% 0.28/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.46 = emptyset )
% 0.28/0.46 => $false ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(vacuousDall_type,type,
% 0.28/0.46 vacuousDall: $o ).
% 0.28/0.46
% 0.28/0.46 thf(vacuousDall,definition,
% 0.28/0.46 ( vacuousDall
% 0.28/0.46 = ( ! [Xphi: $i > $o,Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ emptyset )
% 0.28/0.46 => ( Xphi @ Xx ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(quantDeMorgan1_type,type,
% 0.28/0.46 quantDeMorgan1: $o ).
% 0.28/0.46
% 0.28/0.46 thf(quantDeMorgan1,definition,
% 0.28/0.46 ( quantDeMorgan1
% 0.28/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.28/0.46 ( ~ ! [Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ A )
% 0.28/0.46 => ( Xphi @ Xx ) )
% 0.28/0.46 => ? [Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ A )
% 0.28/0.46 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(quantDeMorgan2_type,type,
% 0.28/0.46 quantDeMorgan2: $o ).
% 0.28/0.46
% 0.28/0.46 thf(quantDeMorgan2,definition,
% 0.28/0.46 ( quantDeMorgan2
% 0.28/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.28/0.46 ( ! [Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ A )
% 0.28/0.46 => ~ ( Xphi @ Xx ) )
% 0.28/0.46 => ~ ? [Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ A )
% 0.28/0.46 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(quantDeMorgan3_type,type,
% 0.28/0.46 quantDeMorgan3: $o ).
% 0.28/0.46
% 0.28/0.46 thf(quantDeMorgan3,definition,
% 0.28/0.46 ( quantDeMorgan3
% 0.28/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.28/0.46 ( ~ ? [Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ A )
% 0.28/0.46 & ( Xphi @ Xx ) )
% 0.28/0.46 => ! [Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ A )
% 0.28/0.46 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(quantDeMorgan4_type,type,
% 0.28/0.46 quantDeMorgan4: $o ).
% 0.28/0.46
% 0.28/0.46 thf(quantDeMorgan4,definition,
% 0.28/0.46 ( quantDeMorgan4
% 0.28/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.28/0.46 ( ? [Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ A )
% 0.28/0.46 & ~ ( Xphi @ Xx ) )
% 0.28/0.46 => ~ ! [Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ A )
% 0.28/0.46 => ( Xphi @ Xx ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(prop2setI_type,type,
% 0.28/0.46 prop2setI: $o ).
% 0.28/0.46
% 0.28/0.46 thf(prop2setI,definition,
% 0.28/0.46 ( prop2setI
% 0.28/0.46 = ( ! [Xphi: $o] :
% 0.28/0.46 ( Xphi
% 0.28/0.46 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(set2prop_type,type,
% 0.28/0.46 set2prop: $i > $o ).
% 0.28/0.46
% 0.28/0.46 thf(prop2set2propI_type,type,
% 0.28/0.46 prop2set2propI: $o ).
% 0.28/0.46
% 0.28/0.46 thf(prop2set2propI,definition,
% 0.28/0.46 ( prop2set2propI
% 0.28/0.46 = ( ! [Xphi: $o] :
% 0.28/0.46 ( Xphi
% 0.28/0.46 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(notdexE_type,type,
% 0.28/0.46 notdexE: $o ).
% 0.28/0.46
% 0.28/0.46 thf(notdexE,definition,
% 0.28/0.46 ( notdexE
% 0.28/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.28/0.46 ( ~ ? [Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ A )
% 0.28/0.46 & ( Xphi @ Xx ) )
% 0.28/0.46 => ! [Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ A )
% 0.28/0.46 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(notdallE_type,type,
% 0.28/0.46 notdallE: $o ).
% 0.28/0.46
% 0.28/0.46 thf(notdallE,definition,
% 0.28/0.46 ( notdallE
% 0.28/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.28/0.46 ( ~ ! [Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ A )
% 0.28/0.46 => ( Xphi @ Xx ) )
% 0.28/0.46 => ? [Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ A )
% 0.28/0.46 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(exuI1_type,type,
% 0.28/0.46 exuI1: $o ).
% 0.28/0.46
% 0.28/0.46 thf(exuI1,definition,
% 0.28/0.46 ( exuI1
% 0.28/0.46 = ( ! [Xphi: $i > $o] :
% 0.28/0.46 ( ? [Xx: $i] :
% 0.28/0.46 ( ( Xphi @ Xx )
% 0.28/0.46 & ! [Xy: $i] :
% 0.28/0.46 ( ( Xphi @ Xy )
% 0.28/0.46 => ( Xx = Xy ) ) )
% 0.28/0.46 => ( exu
% 0.28/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(exuI3_type,type,
% 0.28/0.46 exuI3: $o ).
% 0.28/0.46
% 0.28/0.46 thf(exuI3,definition,
% 0.28/0.46 ( exuI3
% 0.28/0.46 = ( ! [Xphi: $i > $o] :
% 0.28/0.46 ( ? [Xx: $i] : ( Xphi @ Xx )
% 0.28/0.46 => ( ! [Xx: $i,Xy: $i] :
% 0.28/0.46 ( ( Xphi @ Xx )
% 0.28/0.46 => ( ( Xphi @ Xy )
% 0.28/0.46 => ( Xx = Xy ) ) )
% 0.28/0.46 => ( exu
% 0.28/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(exuI2_type,type,
% 0.28/0.46 exuI2: $o ).
% 0.28/0.46
% 0.28/0.46 thf(exuI2,definition,
% 0.28/0.46 ( exuI2
% 0.28/0.46 = ( ! [Xphi: $i > $o] :
% 0.28/0.46 ( ? [Xx: $i] :
% 0.28/0.46 ! [Xy: $i] :
% 0.28/0.46 ( ( Xphi @ Xy )
% 0.28/0.46 <=> ( Xy = Xx ) )
% 0.28/0.46 => ( exu
% 0.28/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(inCongP_type,type,
% 0.28/0.46 inCongP: $o ).
% 0.28/0.46
% 0.28/0.46 thf(inCongP,definition,
% 0.28/0.46 ( inCongP
% 0.28/0.46 = ( ! [A: $i,B: $i] :
% 0.28/0.46 ( ( A = B )
% 0.28/0.46 => ! [Xx: $i,Xy: $i] :
% 0.28/0.46 ( ( Xx = Xy )
% 0.28/0.46 => ( ( in @ Xx @ A )
% 0.28/0.46 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(in__Cong_type,type,
% 0.28/0.46 in__Cong: $o ).
% 0.28/0.46
% 0.28/0.46 thf(in__Cong,definition,
% 0.28/0.46 ( in__Cong
% 0.28/0.46 = ( ! [A: $i,B: $i] :
% 0.28/0.46 ( ( A = B )
% 0.28/0.46 => ! [Xx: $i,Xy: $i] :
% 0.28/0.46 ( ( Xx = Xy )
% 0.28/0.46 => ( ( in @ Xx @ A )
% 0.28/0.46 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(exuE3u_type,type,
% 0.28/0.46 exuE3u: $o ).
% 0.28/0.46
% 0.28/0.46 thf(exuE3u,definition,
% 0.28/0.46 ( exuE3u
% 0.28/0.46 = ( ! [Xphi: $i > $o] :
% 0.28/0.46 ( ( exu
% 0.28/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.46 => ! [Xx: $i,Xy: $i] :
% 0.28/0.46 ( ( Xphi @ Xx )
% 0.28/0.46 => ( ( Xphi @ Xy )
% 0.28/0.46 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(exu__Cong_type,type,
% 0.28/0.46 exu__Cong: $o ).
% 0.28/0.46
% 0.28/0.46 thf(exu__Cong,definition,
% 0.28/0.46 ( exu__Cong
% 0.28/0.46 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.28/0.46 ( ! [Xx: $i,Xy: $i] :
% 0.28/0.46 ( ( Xx = Xy )
% 0.28/0.46 => ( ( Xphi @ Xx )
% 0.28/0.46 <=> ( Xpsi @ Xy ) ) )
% 0.28/0.46 => ( ( exu
% 0.28/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.46 <=> ( exu
% 0.28/0.46 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(emptyset__Cong_type,type,
% 0.28/0.46 emptyset__Cong: $o ).
% 0.28/0.46
% 0.28/0.46 thf(emptyset__Cong,definition,
% 0.28/0.46 ( emptyset__Cong
% 0.28/0.46 = ( emptyset = emptyset ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(setadjoin__Cong_type,type,
% 0.28/0.46 setadjoin__Cong: $o ).
% 0.28/0.46
% 0.28/0.46 thf(setadjoin__Cong,definition,
% 0.28/0.46 ( setadjoin__Cong
% 0.28/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.28/0.46 ( ( Xx = Xy )
% 0.28/0.46 => ! [Xz: $i,Xu: $i] :
% 0.28/0.46 ( ( Xz = Xu )
% 0.28/0.46 => ( ( setadjoin @ Xx @ Xz )
% 0.28/0.46 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(powerset__Cong_type,type,
% 0.28/0.46 powerset__Cong: $o ).
% 0.28/0.46
% 0.28/0.46 thf(powerset__Cong,definition,
% 0.28/0.46 ( powerset__Cong
% 0.28/0.46 = ( ! [A: $i,B: $i] :
% 0.28/0.46 ( ( A = B )
% 0.28/0.46 => ( ( powerset @ A )
% 0.28/0.46 = ( powerset @ B ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(setunion__Cong_type,type,
% 0.28/0.46 setunion__Cong: $o ).
% 0.28/0.46
% 0.28/0.46 thf(setunion__Cong,definition,
% 0.28/0.46 ( setunion__Cong
% 0.28/0.46 = ( ! [A: $i,B: $i] :
% 0.28/0.46 ( ( A = B )
% 0.28/0.46 => ( ( setunion @ A )
% 0.28/0.46 = ( setunion @ B ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(omega__Cong_type,type,
% 0.28/0.46 omega__Cong: $o ).
% 0.28/0.46
% 0.28/0.46 thf(omega__Cong,definition,
% 0.28/0.46 ( omega__Cong
% 0.28/0.46 = ( omega = omega ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(exuEu_type,type,
% 0.28/0.46 exuEu: $o ).
% 0.28/0.46
% 0.28/0.46 thf(exuEu,definition,
% 0.28/0.46 ( exuEu
% 0.28/0.46 = ( ! [Xphi: $i > $o] :
% 0.28/0.46 ( ( exu
% 0.28/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.46 => ! [Xx: $i,Xy: $i] :
% 0.28/0.46 ( ( Xphi @ Xx )
% 0.28/0.46 => ( ( Xphi @ Xy )
% 0.28/0.46 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(descr__Cong_type,type,
% 0.28/0.46 descr__Cong: $o ).
% 0.28/0.46
% 0.28/0.46 thf(descr__Cong,definition,
% 0.28/0.46 ( descr__Cong
% 0.28/0.46 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.28/0.46 ( ! [Xx: $i,Xy: $i] :
% 0.28/0.46 ( ( Xx = Xy )
% 0.28/0.46 => ( ( Xphi @ Xx )
% 0.28/0.46 <=> ( Xpsi @ Xy ) ) )
% 0.28/0.46 => ( ( exu
% 0.28/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.46 => ( ( exu
% 0.28/0.46 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 0.28/0.46 => ( ( descr
% 0.28/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.46 = ( descr
% 0.28/0.46 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(dsetconstr__Cong_type,type,
% 0.28/0.46 dsetconstr__Cong: $o ).
% 0.28/0.46
% 0.28/0.46 thf(dsetconstr__Cong,definition,
% 0.28/0.46 ( dsetconstr__Cong
% 0.28/0.46 = ( ! [A: $i,B: $i] :
% 0.28/0.46 ( ( A = B )
% 0.28/0.46 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.28/0.46 ( ! [Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ A )
% 0.28/0.46 => ! [Xy: $i] :
% 0.28/0.46 ( ( in @ Xy @ B )
% 0.28/0.46 => ( ( Xx = Xy )
% 0.28/0.46 => ( ( Xphi @ Xx )
% 0.28/0.46 <=> ( Xpsi @ Xy ) ) ) ) )
% 0.28/0.46 => ( ( dsetconstr @ A
% 0.28/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.46 = ( dsetconstr @ B
% 0.28/0.46 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(subset_type,type,
% 0.28/0.46 subset: $i > $i > $o ).
% 0.28/0.46
% 0.28/0.46 thf(disjoint_type,type,
% 0.28/0.46 disjoint: $i > $i > $o ).
% 0.28/0.46
% 0.28/0.46 thf(setsmeet_type,type,
% 0.28/0.46 setsmeet: $i > $i > $o ).
% 0.28/0.46
% 0.28/0.46 thf(subsetI1_type,type,
% 0.28/0.46 subsetI1: $o ).
% 0.28/0.46
% 0.28/0.46 thf(subsetI1,definition,
% 0.28/0.46 ( subsetI1
% 0.28/0.46 = ( ! [A: $i,B: $i] :
% 0.28/0.46 ( ! [Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ A )
% 0.28/0.46 => ( in @ Xx @ B ) )
% 0.28/0.46 => ( subset @ A @ B ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(eqimpsubset2_type,type,
% 0.28/0.46 eqimpsubset2: $o ).
% 0.28/0.46
% 0.28/0.46 thf(eqimpsubset2,definition,
% 0.28/0.46 ( eqimpsubset2
% 0.28/0.46 = ( ! [A: $i,B: $i] :
% 0.28/0.46 ( ( A = B )
% 0.28/0.46 => ( subset @ B @ A ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(eqimpsubset1_type,type,
% 0.28/0.46 eqimpsubset1: $o ).
% 0.28/0.46
% 0.28/0.46 thf(eqimpsubset1,definition,
% 0.28/0.46 ( eqimpsubset1
% 0.28/0.46 = ( ! [A: $i,B: $i] :
% 0.28/0.46 ( ( A = B )
% 0.28/0.46 => ( subset @ A @ B ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(subsetI2_type,type,
% 0.28/0.46 subsetI2: $o ).
% 0.28/0.46
% 0.28/0.46 thf(subsetI2,definition,
% 0.28/0.46 ( subsetI2
% 0.28/0.46 = ( ! [A: $i,B: $i] :
% 0.28/0.46 ( ! [Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ A )
% 0.28/0.46 => ( in @ Xx @ B ) )
% 0.28/0.46 => ( subset @ A @ B ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(emptysetsubset_type,type,
% 0.28/0.46 emptysetsubset: $o ).
% 0.28/0.46
% 0.28/0.46 thf(emptysetsubset,definition,
% 0.28/0.46 ( emptysetsubset
% 0.28/0.46 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(subsetE_type,type,
% 0.28/0.46 subsetE: $o ).
% 0.28/0.46
% 0.28/0.46 thf(subsetE,definition,
% 0.28/0.46 ( subsetE
% 0.28/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.46 ( ( subset @ A @ B )
% 0.28/0.46 => ( ( in @ Xx @ A )
% 0.28/0.46 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(subsetE2,conjecture,
% 0.28/0.46 ( setextAx
% 0.28/0.46 => ( emptysetAx
% 0.28/0.46 => ( setadjoinAx
% 0.28/0.46 => ( powersetAx
% 0.28/0.46 => ( setunionAx
% 0.28/0.46 => ( omega0Ax
% 0.28/0.46 => ( omegaSAx
% 0.28/0.46 => ( omegaIndAx
% 0.28/0.46 => ( replAx
% 0.28/0.46 => ( foundationAx
% 0.28/0.46 => ( wellorderingAx
% 0.28/0.46 => ( descrp
% 0.28/0.46 => ( dsetconstrI
% 0.28/0.46 => ( dsetconstrEL
% 0.28/0.46 => ( dsetconstrER
% 0.28/0.46 => ( exuE1
% 0.28/0.46 => ( prop2setE
% 0.28/0.46 => ( emptysetE
% 0.28/0.46 => ( emptysetimpfalse
% 0.28/0.46 => ( notinemptyset
% 0.28/0.46 => ( exuE3e
% 0.28/0.46 => ( setext
% 0.28/0.46 => ( emptyI
% 0.28/0.46 => ( noeltsimpempty
% 0.28/0.46 => ( setbeta
% 0.28/0.46 => ( nonemptyE1
% 0.28/0.46 => ( nonemptyI
% 0.28/0.46 => ( nonemptyI1
% 0.28/0.46 => ( setadjoinIL
% 0.28/0.46 => ( emptyinunitempty
% 0.28/0.46 => ( setadjoinIR
% 0.28/0.46 => ( setadjoinE
% 0.28/0.46 => ( setadjoinOr
% 0.28/0.46 => ( setoftrueEq
% 0.28/0.46 => ( powersetI
% 0.28/0.46 => ( emptyinPowerset
% 0.28/0.46 => ( emptyInPowerset
% 0.28/0.46 => ( powersetE
% 0.28/0.46 => ( setunionI
% 0.28/0.46 => ( setunionE
% 0.28/0.46 => ( subPowSU
% 0.28/0.46 => ( exuE2
% 0.28/0.46 => ( nonemptyImpWitness
% 0.28/0.46 => ( uniqinunit
% 0.28/0.46 => ( notinsingleton
% 0.28/0.46 => ( eqinunit
% 0.28/0.46 => ( singletonsswitch
% 0.28/0.46 => ( upairsetE
% 0.28/0.46 => ( upairsetIL
% 0.28/0.46 => ( upairsetIR
% 0.28/0.46 => ( emptyE1
% 0.28/0.46 => ( vacuousDall
% 0.28/0.46 => ( quantDeMorgan1
% 0.28/0.46 => ( quantDeMorgan2
% 0.28/0.46 => ( quantDeMorgan3
% 0.28/0.46 => ( quantDeMorgan4
% 0.28/0.46 => ( prop2setI
% 0.28/0.46 => ( prop2set2propI
% 0.28/0.46 => ( notdexE
% 0.28/0.46 => ( notdallE
% 0.28/0.46 => ( exuI1
% 0.28/0.46 => ( exuI3
% 0.28/0.46 => ( exuI2
% 0.28/0.46 => ( inCongP
% 0.28/0.46 => ( in__Cong
% 0.28/0.46 => ( exuE3u
% 0.28/0.46 => ( exu__Cong
% 0.28/0.46 => ( emptyset__Cong
% 0.28/0.46 => ( setadjoin__Cong
% 0.28/0.46 => ( powerset__Cong
% 0.28/0.46 => ( setunion__Cong
% 0.28/0.46 => ( omega__Cong
% 0.28/0.46 => ( exuEu
% 0.28/0.46 => ( descr__Cong
% 0.28/0.46 => ( dsetconstr__Cong
% 0.28/0.46 => ( subsetI1
% 0.28/0.46 => ( eqimpsubset2
% 0.28/0.46 => ( eqimpsubset1
% 0.28/0.46 => ( subsetI2
% 0.28/0.46 => ( emptysetsubset
% 0.28/0.46 => ( subsetE
% 0.28/0.46 => ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.46 ( ( subset @ A @ B )
% 0.28/0.46 => ( ~ ( in @ Xx @ B )
% 0.28/0.46 => ~ ( in @ Xx @ A ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 %------------------------------------------------------------------------------
% 0.28/0.46 ------------------------
% 2.34/1.43 ---- Embedded in THF ---
% 2.34/1.43 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.34/1.43 %%% Generated on Tue Feb 24 12:27:01 EST 2026
% 2.34/1.43 %%% using '$$dhol' embedding, version 1.3.0.
% 2.34/1.43 %%% Logic specification used:
% 2.34/1.43 %%% thf(spec, logic, $$dhol).
% 2.34/1.43
% 2.34/1.43 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.cd1eMribCG/DTF2DTF26070.p
% See solution above
% 2.34/1.43 ------------------------
% 2.34/1.45 ---- Cleaned THF ---
% 2.34/1.45 thf(in_type,type,
% 2.34/1.45 in: $i > $i > $o ).
% 2.34/1.45
% 2.34/1.45 thf(exu_type,type,
% 2.34/1.45 exu: ( $i > $o ) > $o ).
% 2.34/1.45
% 2.34/1.45 thf(exu,definition,
% 2.34/1.45 ( exu
% 2.34/1.45 = ( ^ [Xphi: $i > $o] :
% 2.34/1.45 ? [Xx: $i] :
% 2.34/1.45 ( ( Xphi @ Xx )
% 2.34/1.45 & ! [Xy: $i] :
% 2.34/1.45 ( ( Xphi @ Xy )
% 2.34/1.45 => ( Xx = Xy ) ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(setextAx_type,type,
% 2.34/1.45 setextAx: $o ).
% 2.34/1.45
% 2.34/1.45 thf(setextAx,definition,
% 2.34/1.45 ( setextAx
% 2.34/1.45 = ( ! [A: $i,B: $i] :
% 2.34/1.45 ( ! [Xx: $i] :
% 2.34/1.45 ( ( in @ Xx @ A )
% 2.34/1.45 <=> ( in @ Xx @ B ) )
% 2.34/1.45 => ( A = B ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(emptyset_type,type,
% 2.34/1.45 emptyset: $i ).
% 2.34/1.45
% 2.34/1.45 thf(emptysetAx_type,type,
% 2.34/1.45 emptysetAx: $o ).
% 2.34/1.45
% 2.34/1.45 thf(emptysetAx,definition,
% 2.34/1.45 ( emptysetAx
% 2.34/1.45 = ( ! [Xx: $i] :
% 2.34/1.45 ~ ( in @ Xx @ emptyset ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(setadjoin_type,type,
% 2.34/1.45 setadjoin: $i > $i > $i ).
% 2.34/1.45
% 2.34/1.45 thf(setadjoinAx_type,type,
% 2.34/1.45 setadjoinAx: $o ).
% 2.34/1.45
% 2.34/1.45 thf(setadjoinAx,definition,
% 2.34/1.45 ( setadjoinAx
% 2.34/1.45 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.34/1.45 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.34/1.45 <=> ( ( Xy = Xx )
% 2.34/1.45 | ( in @ Xy @ A ) ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(powerset_type,type,
% 2.34/1.45 powerset: $i > $i ).
% 2.34/1.45
% 2.34/1.45 thf(powersetAx_type,type,
% 2.34/1.45 powersetAx: $o ).
% 2.34/1.45
% 2.34/1.45 thf(powersetAx,definition,
% 2.34/1.45 ( powersetAx
% 2.34/1.45 = ( ! [A: $i,B: $i] :
% 2.34/1.45 ( ( in @ B @ ( powerset @ A ) )
% 2.34/1.45 <=> ! [Xx: $i] :
% 2.34/1.45 ( ( in @ Xx @ B )
% 2.34/1.45 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(setunion_type,type,
% 2.34/1.45 setunion: $i > $i ).
% 2.34/1.45
% 2.34/1.45 thf(setunionAx_type,type,
% 2.34/1.45 setunionAx: $o ).
% 2.34/1.45
% 2.34/1.45 thf(setunionAx,definition,
% 2.34/1.45 ( setunionAx
% 2.34/1.45 = ( ! [A: $i,Xx: $i] :
% 2.34/1.45 ( ( in @ Xx @ ( setunion @ A ) )
% 2.34/1.45 <=> ? [B: $i] :
% 2.34/1.45 ( ( in @ Xx @ B )
% 2.34/1.45 & ( in @ B @ A ) ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(omega_type,type,
% 2.34/1.45 omega: $i ).
% 2.34/1.45
% 2.34/1.45 thf(omega0Ax_type,type,
% 2.34/1.45 omega0Ax: $o ).
% 2.34/1.45
% 2.34/1.45 thf(omega0Ax,definition,
% 2.34/1.45 ( omega0Ax
% 2.34/1.45 = ( in @ emptyset @ omega ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(omegaSAx_type,type,
% 2.34/1.45 omegaSAx: $o ).
% 2.34/1.45
% 2.34/1.45 thf(omegaSAx,definition,
% 2.34/1.45 ( omegaSAx
% 2.34/1.45 = ( ! [Xx: $i] :
% 2.34/1.45 ( ( in @ Xx @ omega )
% 2.34/1.45 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(omegaIndAx_type,type,
% 2.34/1.45 omegaIndAx: $o ).
% 2.34/1.45
% 2.34/1.45 thf(omegaIndAx,definition,
% 2.34/1.45 ( omegaIndAx
% 2.34/1.45 = ( ! [A: $i] :
% 2.34/1.45 ( ( ( in @ emptyset @ A )
% 2.34/1.45 & ! [Xx: $i] :
% 2.34/1.45 ( ( ( in @ Xx @ omega )
% 2.34/1.45 & ( in @ Xx @ A ) )
% 2.34/1.45 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 2.34/1.45 => ! [Xx: $i] :
% 2.34/1.45 ( ( in @ Xx @ omega )
% 2.34/1.45 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(replAx_type,type,
% 2.34/1.45 replAx: $o ).
% 2.34/1.45
% 2.34/1.45 thf(replAx,definition,
% 2.34/1.45 ( replAx
% 2.34/1.45 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 2.34/1.45 ( ! [Xx: $i] :
% 2.34/1.45 ( ( in @ Xx @ A )
% 2.34/1.45 => ( exu
% 2.34/1.45 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 2.34/1.45 => ? [B: $i] :
% 2.34/1.45 ! [Xx: $i] :
% 2.34/1.45 ( ( in @ Xx @ B )
% 2.34/1.45 <=> ? [Xy: $i] :
% 2.34/1.45 ( ( in @ Xy @ A )
% 2.34/1.45 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(foundationAx_type,type,
% 2.34/1.45 foundationAx: $o ).
% 2.34/1.45
% 2.34/1.45 thf(foundationAx,definition,
% 2.34/1.45 ( foundationAx
% 2.34/1.45 = ( ! [A: $i] :
% 2.34/1.45 ( ? [Xx: $i] : ( in @ Xx @ A )
% 2.34/1.45 => ? [B: $i] :
% 2.34/1.45 ( ( in @ B @ A )
% 2.34/1.45 & ~ ? [Xx: $i] :
% 2.34/1.45 ( ( in @ Xx @ B )
% 2.34/1.45 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(wellorderingAx_type,type,
% 2.34/1.45 wellorderingAx: $o ).
% 2.34/1.45
% 2.34/1.45 thf(wellorderingAx,definition,
% 2.34/1.45 ( wellorderingAx
% 2.34/1.45 = ( ! [A: $i] :
% 2.34/1.45 ? [B: $i] :
% 2.34/1.45 ( ! [C: $i] :
% 2.34/1.45 ( ( in @ C @ B )
% 2.34/1.45 => ! [Xx: $i] :
% 2.34/1.45 ( ( in @ Xx @ C )
% 2.34/1.45 => ( in @ Xx @ A ) ) )
% 2.34/1.45 & ! [Xx: $i,Xy: $i] :
% 2.34/1.45 ( ( ( in @ Xx @ A )
% 2.34/1.45 & ( in @ Xy @ A ) )
% 2.34/1.45 => ( ! [C: $i] :
% 2.34/1.45 ( ( in @ C @ B )
% 2.34/1.45 => ( ( in @ Xx @ C )
% 2.34/1.45 <=> ( in @ Xy @ C ) ) )
% 2.34/1.45 => ( Xx = Xy ) ) )
% 2.34/1.45 & ! [C: $i,D: $i] :
% 2.34/1.45 ( ( ( in @ C @ B )
% 2.34/1.45 & ( in @ D @ B ) )
% 2.34/1.45 => ( ! [Xx: $i] :
% 2.34/1.45 ( ( in @ Xx @ C )
% 2.34/1.45 => ( in @ Xx @ D ) )
% 2.34/1.45 | ! [Xx: $i] :
% 2.34/1.45 ( ( in @ Xx @ D )
% 2.34/1.45 => ( in @ Xx @ C ) ) ) )
% 2.34/1.45 & ! [C: $i] :
% 2.34/1.45 ( ( ! [Xx: $i] :
% 2.34/1.45 ( ( in @ Xx @ C )
% 2.34/1.45 => ( in @ Xx @ A ) )
% 2.34/1.45 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 2.34/1.45 => ? [D: $i,Xx: $i] :
% 2.34/1.45 ( ( in @ D @ B )
% 2.34/1.45 & ( in @ Xx @ C )
% 2.34/1.45 & ~ ? [Xy: $i] :
% 2.34/1.45 ( ( in @ Xy @ D )
% 2.34/1.45 & ( in @ Xy @ C ) )
% 2.34/1.45 & ! [E: $i] :
% 2.34/1.45 ( ( in @ E @ B )
% 2.34/1.45 => ( ! [Xy: $i] :
% 2.34/1.45 ( ( in @ Xy @ E )
% 2.34/1.45 => ( in @ Xy @ D ) )
% 2.34/1.45 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(descr_type,type,
% 2.34/1.45 descr: ( $i > $o ) > $i ).
% 2.34/1.45
% 2.34/1.45 thf(descrp_type,type,
% 2.34/1.45 descrp: $o ).
% 2.34/1.45
% 2.34/1.45 thf(descrp,definition,
% 2.34/1.45 ( descrp
% 2.34/1.45 = ( ! [Xphi: $i > $o] :
% 2.34/1.45 ( ( exu
% 2.34/1.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.34/1.45 => ( Xphi
% 2.34/1.45 @ ( descr
% 2.34/1.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(dsetconstr_type,type,
% 2.34/1.45 dsetconstr: $i > ( $i > $o ) > $i ).
% 2.34/1.45
% 2.34/1.45 thf(dsetconstrI_type,type,
% 2.34/1.45 dsetconstrI: $o ).
% 2.34/1.45
% 2.34/1.45 thf(dsetconstrI,definition,
% 2.34/1.45 ( dsetconstrI
% 2.34/1.45 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.34/1.45 ( ( in @ Xx @ A )
% 2.34/1.45 => ( ( Xphi @ Xx )
% 2.34/1.45 => ( in @ Xx
% 2.34/1.45 @ ( dsetconstr @ A
% 2.34/1.45 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(dsetconstrEL_type,type,
% 2.34/1.45 dsetconstrEL: $o ).
% 2.34/1.45
% 2.34/1.45 thf(dsetconstrEL,definition,
% 2.34/1.45 ( dsetconstrEL
% 2.34/1.45 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.34/1.45 ( ( in @ Xx
% 2.34/1.45 @ ( dsetconstr @ A
% 2.34/1.45 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.34/1.45 => ( in @ Xx @ A ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(dsetconstrER_type,type,
% 2.34/1.45 dsetconstrER: $o ).
% 2.34/1.45
% 2.34/1.45 thf(dsetconstrER,definition,
% 2.34/1.45 ( dsetconstrER
% 2.34/1.45 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.34/1.45 ( ( in @ Xx
% 2.34/1.45 @ ( dsetconstr @ A
% 2.34/1.45 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.34/1.45 => ( Xphi @ Xx ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(exuE1_type,type,
% 2.34/1.45 exuE1: $o ).
% 2.34/1.45
% 2.34/1.45 thf(exuE1,definition,
% 2.34/1.45 ( exuE1
% 2.34/1.45 = ( ! [Xphi: $i > $o] :
% 2.34/1.45 ( ( exu
% 2.34/1.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.34/1.45 => ? [Xx: $i] :
% 2.34/1.45 ( ( Xphi @ Xx )
% 2.34/1.45 & ! [Xy: $i] :
% 2.34/1.45 ( ( Xphi @ Xy )
% 2.34/1.45 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(prop2set_type,type,
% 2.34/1.45 prop2set: $o > $i ).
% 2.34/1.45
% 2.34/1.45 thf(prop2setE_type,type,
% 2.34/1.45 prop2setE: $o ).
% 2.34/1.45
% 2.34/1.45 thf(prop2setE,definition,
% 2.34/1.45 ( prop2setE
% 2.34/1.45 = ( ! [Xphi: $o,Xx: $i] :
% 2.34/1.45 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 2.34/1.45 => Xphi ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(emptysetE_type,type,
% 2.34/1.45 emptysetE: $o ).
% 2.34/1.45
% 2.34/1.45 thf(emptysetE,definition,
% 2.34/1.45 ( emptysetE
% 2.34/1.45 = ( ! [Xx: $i] :
% 2.34/1.45 ( ( in @ Xx @ emptyset )
% 2.34/1.45 => ! [Xphi: $o] : Xphi ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(emptysetimpfalse_type,type,
% 2.34/1.45 emptysetimpfalse: $o ).
% 2.34/1.45
% 2.34/1.45 thf(emptysetimpfalse,definition,
% 2.34/1.45 ( emptysetimpfalse
% 2.34/1.45 = ( ! [Xx: $i] :
% 2.34/1.45 ( ( in @ Xx @ emptyset )
% 2.34/1.45 => $false ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(notinemptyset_type,type,
% 2.34/1.45 notinemptyset: $o ).
% 2.34/1.45
% 2.34/1.45 thf(notinemptyset,definition,
% 2.34/1.45 ( notinemptyset
% 2.34/1.45 = ( ! [Xx: $i] :
% 2.34/1.45 ~ ( in @ Xx @ emptyset ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(exuE3e_type,type,
% 2.34/1.45 exuE3e: $o ).
% 2.34/1.45
% 2.34/1.45 thf(exuE3e,definition,
% 2.34/1.45 ( exuE3e
% 2.34/1.45 = ( ! [Xphi: $i > $o] :
% 2.34/1.45 ( ( exu
% 2.34/1.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.34/1.45 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(setext_type,type,
% 2.34/1.45 setext: $o ).
% 2.34/1.45
% 2.34/1.45 thf(setext,definition,
% 2.34/1.45 ( setext
% 2.34/1.45 = ( ! [A: $i,B: $i] :
% 2.34/1.45 ( ! [Xx: $i] :
% 2.34/1.45 ( ( in @ Xx @ A )
% 2.34/1.45 => ( in @ Xx @ B ) )
% 2.34/1.45 => ( ! [Xx: $i] :
% 2.34/1.45 ( ( in @ Xx @ B )
% 2.34/1.45 => ( in @ Xx @ A ) )
% 2.34/1.45 => ( A = B ) ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(emptyI_type,type,
% 2.34/1.45 emptyI: $o ).
% 2.34/1.45
% 2.34/1.45 thf(emptyI,definition,
% 2.34/1.45 ( emptyI
% 2.34/1.45 = ( ! [A: $i] :
% 2.34/1.45 ( ! [Xx: $i] :
% 2.34/1.45 ~ ( in @ Xx @ A )
% 2.34/1.45 => ( A = emptyset ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(noeltsimpempty_type,type,
% 2.34/1.45 noeltsimpempty: $o ).
% 2.34/1.45
% 2.34/1.45 thf(noeltsimpempty,definition,
% 2.34/1.45 ( noeltsimpempty
% 2.34/1.45 = ( ! [A: $i] :
% 2.34/1.45 ( ! [Xx: $i] :
% 2.34/1.45 ~ ( in @ Xx @ A )
% 2.34/1.45 => ( A = emptyset ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(setbeta_type,type,
% 2.34/1.45 setbeta: $o ).
% 2.34/1.45
% 2.34/1.45 thf(setbeta,definition,
% 2.34/1.45 ( setbeta
% 2.34/1.45 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.34/1.45 ( ( in @ Xx @ A )
% 2.34/1.45 => ( ( in @ Xx
% 2.34/1.45 @ ( dsetconstr @ A
% 2.34/1.45 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.34/1.45 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(nonempty_type,type,
% 2.34/1.45 nonempty: $i > $o ).
% 2.34/1.45
% 2.34/1.45 thf(nonempty,definition,
% 2.34/1.45 ( nonempty
% 2.34/1.45 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(nonemptyE1_type,type,
% 2.34/1.45 nonemptyE1: $o ).
% 2.34/1.45
% 2.34/1.45 thf(nonemptyE1,definition,
% 2.34/1.45 ( nonemptyE1
% 2.34/1.45 = ( ! [A: $i] :
% 2.34/1.45 ( ( nonempty @ A )
% 2.34/1.45 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(nonemptyI_type,type,
% 2.34/1.45 nonemptyI: $o ).
% 2.34/1.45
% 2.34/1.45 thf(nonemptyI,definition,
% 2.34/1.45 ( nonemptyI
% 2.34/1.45 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.34/1.45 ( ( in @ Xx @ A )
% 2.34/1.45 => ( ( Xphi @ Xx )
% 2.34/1.45 => ( nonempty
% 2.34/1.45 @ ( dsetconstr @ A
% 2.34/1.45 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(nonemptyI1_type,type,
% 2.34/1.45 nonemptyI1: $o ).
% 2.34/1.45
% 2.34/1.45 thf(nonemptyI1,definition,
% 2.34/1.45 ( nonemptyI1
% 2.34/1.45 = ( ! [A: $i] :
% 2.34/1.45 ( ? [Xx: $i] : ( in @ Xx @ A )
% 2.34/1.45 => ( nonempty @ A ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(setadjoinIL_type,type,
% 2.34/1.45 setadjoinIL: $o ).
% 2.34/1.45
% 2.34/1.45 thf(setadjoinIL,definition,
% 2.34/1.45 ( setadjoinIL
% 2.34/1.45 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(emptyinunitempty_type,type,
% 2.34/1.45 emptyinunitempty: $o ).
% 2.34/1.45
% 2.34/1.45 thf(emptyinunitempty,definition,
% 2.34/1.45 ( emptyinunitempty
% 2.34/1.45 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(setadjoinIR_type,type,
% 2.34/1.45 setadjoinIR: $o ).
% 2.34/1.45
% 2.34/1.45 thf(setadjoinIR,definition,
% 2.34/1.45 ( setadjoinIR
% 2.34/1.45 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.34/1.45 ( ( in @ Xy @ A )
% 2.34/1.45 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(setadjoinE_type,type,
% 2.34/1.45 setadjoinE: $o ).
% 2.34/1.45
% 2.34/1.45 thf(setadjoinE,definition,
% 2.34/1.45 ( setadjoinE
% 2.34/1.45 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.34/1.45 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.34/1.45 => ! [Xphi: $o] :
% 2.34/1.45 ( ( ( Xy = Xx )
% 2.34/1.45 => Xphi )
% 2.34/1.45 => ( ( ( in @ Xy @ A )
% 2.34/1.45 => Xphi )
% 2.34/1.45 => Xphi ) ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(setadjoinOr_type,type,
% 2.34/1.45 setadjoinOr: $o ).
% 2.34/1.45
% 2.34/1.45 thf(setadjoinOr,definition,
% 2.34/1.45 ( setadjoinOr
% 2.34/1.45 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.34/1.45 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.34/1.45 => ( ( Xy = Xx )
% 2.34/1.45 | ( in @ Xy @ A ) ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(setoftrueEq_type,type,
% 2.34/1.45 setoftrueEq: $o ).
% 2.34/1.45
% 2.34/1.45 thf(setoftrueEq,definition,
% 2.34/1.45 ( setoftrueEq
% 2.34/1.45 = ( ! [A: $i] :
% 2.34/1.45 ( ( dsetconstr @ A
% 2.34/1.45 @ ^ [Xx: $i] : $true )
% 2.34/1.45 = A ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(powersetI_type,type,
% 2.34/1.45 powersetI: $o ).
% 2.34/1.45
% 2.34/1.45 thf(powersetI,definition,
% 2.34/1.45 ( powersetI
% 2.34/1.45 = ( ! [A: $i,B: $i] :
% 2.34/1.45 ( ! [Xx: $i] :
% 2.34/1.45 ( ( in @ Xx @ B )
% 2.34/1.45 => ( in @ Xx @ A ) )
% 2.34/1.45 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(emptyinPowerset_type,type,
% 2.34/1.45 emptyinPowerset: $o ).
% 2.34/1.45
% 2.34/1.45 thf(emptyinPowerset,definition,
% 2.34/1.45 ( emptyinPowerset
% 2.34/1.45 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(emptyInPowerset_type,type,
% 2.34/1.45 emptyInPowerset: $o ).
% 2.34/1.45
% 2.34/1.45 thf(emptyInPowerset,definition,
% 2.34/1.45 ( emptyInPowerset
% 2.34/1.45 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(powersetE_type,type,
% 2.34/1.45 powersetE: $o ).
% 2.34/1.45
% 2.34/1.45 thf(powersetE,definition,
% 2.34/1.45 ( powersetE
% 2.34/1.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.34/1.45 ( ( in @ B @ ( powerset @ A ) )
% 2.34/1.45 => ( ( in @ Xx @ B )
% 2.34/1.45 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(setunionI_type,type,
% 2.34/1.45 setunionI: $o ).
% 2.34/1.45
% 2.34/1.45 thf(setunionI,definition,
% 2.34/1.45 ( setunionI
% 2.34/1.45 = ( ! [A: $i,Xx: $i,B: $i] :
% 2.34/1.45 ( ( in @ Xx @ B )
% 2.34/1.45 => ( ( in @ B @ A )
% 2.34/1.45 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(setunionE_type,type,
% 2.34/1.45 setunionE: $o ).
% 2.34/1.45
% 2.34/1.45 thf(setunionE,definition,
% 2.34/1.45 ( setunionE
% 2.34/1.45 = ( ! [A: $i,Xx: $i] :
% 2.34/1.45 ( ( in @ Xx @ ( setunion @ A ) )
% 2.34/1.45 => ! [Xphi: $o] :
% 2.34/1.45 ( ! [B: $i] :
% 2.34/1.45 ( ( in @ Xx @ B )
% 2.34/1.45 => ( ( in @ B @ A )
% 2.34/1.45 => Xphi ) )
% 2.34/1.45 => Xphi ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(subPowSU_type,type,
% 2.34/1.45 subPowSU: $o ).
% 2.34/1.45
% 2.34/1.45 thf(subPowSU,definition,
% 2.34/1.45 ( subPowSU
% 2.34/1.45 = ( ! [A: $i,Xx: $i] :
% 2.34/1.45 ( ( in @ Xx @ A )
% 2.34/1.45 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(exuE2_type,type,
% 2.34/1.45 exuE2: $o ).
% 2.34/1.45
% 2.34/1.45 thf(exuE2,definition,
% 2.34/1.45 ( exuE2
% 2.34/1.45 = ( ! [Xphi: $i > $o] :
% 2.34/1.45 ( ( exu
% 2.34/1.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.34/1.45 => ? [Xx: $i] :
% 2.34/1.45 ! [Xy: $i] :
% 2.34/1.45 ( ( Xphi @ Xy )
% 2.34/1.45 <=> ( Xy = Xx ) ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(nonemptyImpWitness_type,type,
% 2.34/1.45 nonemptyImpWitness: $o ).
% 2.34/1.45
% 2.34/1.45 thf(nonemptyImpWitness,definition,
% 2.34/1.45 ( nonemptyImpWitness
% 2.34/1.45 = ( ! [A: $i] :
% 2.34/1.45 ( ( nonempty @ A )
% 2.34/1.45 => ? [Xx: $i] :
% 2.34/1.45 ( ( in @ Xx @ A )
% 2.34/1.45 & $true ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(uniqinunit_type,type,
% 2.34/1.45 uniqinunit: $o ).
% 2.34/1.45
% 2.34/1.45 thf(uniqinunit,definition,
% 2.34/1.45 ( uniqinunit
% 2.34/1.45 = ( ! [Xx: $i,Xy: $i] :
% 2.34/1.45 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.34/1.45 => ( Xx = Xy ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(notinsingleton_type,type,
% 2.34/1.45 notinsingleton: $o ).
% 2.34/1.45
% 2.34/1.45 thf(notinsingleton,definition,
% 2.34/1.45 ( notinsingleton
% 2.34/1.45 = ( ! [Xx: $i,Xy: $i] :
% 2.34/1.45 ( ( Xx != Xy )
% 2.34/1.45 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(eqinunit_type,type,
% 2.34/1.45 eqinunit: $o ).
% 2.34/1.45
% 2.34/1.45 thf(eqinunit,definition,
% 2.34/1.45 ( eqinunit
% 2.34/1.45 = ( ! [Xx: $i,Xy: $i] :
% 2.34/1.45 ( ( Xx = Xy )
% 2.34/1.45 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(singletonsswitch_type,type,
% 2.34/1.45 singletonsswitch: $o ).
% 2.34/1.45
% 2.34/1.45 thf(singletonsswitch,definition,
% 2.34/1.45 ( singletonsswitch
% 2.34/1.45 = ( ! [Xx: $i,Xy: $i] :
% 2.34/1.45 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.34/1.45 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(upairsetE_type,type,
% 2.34/1.45 upairsetE: $o ).
% 2.34/1.45
% 2.34/1.45 thf(upairsetE,definition,
% 2.34/1.45 ( upairsetE
% 2.34/1.45 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.34/1.45 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 2.34/1.45 => ( ( Xz = Xx )
% 2.34/1.45 | ( Xz = Xy ) ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(upairsetIL_type,type,
% 2.34/1.45 upairsetIL: $o ).
% 2.34/1.45
% 2.34/1.45 thf(upairsetIL,definition,
% 2.34/1.45 ( upairsetIL
% 2.34/1.45 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(upairsetIR_type,type,
% 2.34/1.45 upairsetIR: $o ).
% 2.34/1.45
% 2.34/1.45 thf(upairsetIR,definition,
% 2.34/1.45 ( upairsetIR
% 2.34/1.45 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(emptyE1_type,type,
% 2.34/1.45 emptyE1: $o ).
% 2.34/1.45
% 2.34/1.45 thf(emptyE1,definition,
% 2.34/1.45 ( emptyE1
% 2.34/1.45 = ( ! [A: $i,Xphi: $i > $o] :
% 2.34/1.45 ( ? [Xx: $i] :
% 2.34/1.45 ( ( in @ Xx @ A )
% 2.34/1.45 & ( Xphi @ Xx ) )
% 2.34/1.45 => ( ( ( dsetconstr @ A
% 2.34/1.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.34/1.45 = emptyset )
% 2.34/1.45 => $false ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(vacuousDall_type,type,
% 2.34/1.45 vacuousDall: $o ).
% 2.34/1.45
% 2.34/1.45 thf(vacuousDall,definition,
% 2.34/1.45 ( vacuousDall
% 2.34/1.45 = ( ! [Xphi: $i > $o,Xx: $i] :
% 2.34/1.45 ( ( in @ Xx @ emptyset )
% 2.34/1.45 => ( Xphi @ Xx ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(quantDeMorgan1_type,type,
% 2.34/1.45 quantDeMorgan1: $o ).
% 2.34/1.45
% 2.34/1.45 thf(quantDeMorgan1,definition,
% 2.34/1.45 ( quantDeMorgan1
% 2.34/1.45 = ( ! [A: $i,Xphi: $i > $o] :
% 2.34/1.45 ( ~ ! [Xx: $i] :
% 2.34/1.45 ( ( in @ Xx @ A )
% 2.34/1.45 => ( Xphi @ Xx ) )
% 2.34/1.45 => ? [Xx: $i] :
% 2.34/1.45 ( ( in @ Xx @ A )
% 2.34/1.45 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(quantDeMorgan2_type,type,
% 2.34/1.45 quantDeMorgan2: $o ).
% 2.34/1.45
% 2.34/1.45 thf(quantDeMorgan2,definition,
% 2.34/1.45 ( quantDeMorgan2
% 2.34/1.45 = ( ! [A: $i,Xphi: $i > $o] :
% 2.34/1.45 ( ! [Xx: $i] :
% 2.34/1.45 ( ( in @ Xx @ A )
% 2.34/1.45 => ~ ( Xphi @ Xx ) )
% 2.34/1.45 => ~ ? [Xx: $i] :
% 2.34/1.45 ( ( in @ Xx @ A )
% 2.34/1.45 & ( Xphi @ Xx ) ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(quantDeMorgan3_type,type,
% 2.34/1.45 quantDeMorgan3: $o ).
% 2.34/1.45
% 2.34/1.45 thf(quantDeMorgan3,definition,
% 2.34/1.45 ( quantDeMorgan3
% 2.34/1.45 = ( ! [A: $i,Xphi: $i > $o] :
% 2.34/1.45 ( ~ ? [Xx: $i] :
% 2.34/1.45 ( ( in @ Xx @ A )
% 2.34/1.45 & ( Xphi @ Xx ) )
% 2.34/1.45 => ! [Xx: $i] :
% 2.34/1.45 ( ( in @ Xx @ A )
% 2.34/1.45 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(quantDeMorgan4_type,type,
% 2.34/1.45 quantDeMorgan4: $o ).
% 2.34/1.45
% 2.34/1.45 thf(quantDeMorgan4,definition,
% 2.34/1.45 ( quantDeMorgan4
% 2.34/1.45 = ( ! [A: $i,Xphi: $i > $o] :
% 2.34/1.45 ( ? [Xx: $i] :
% 2.34/1.45 ( ( in @ Xx @ A )
% 2.34/1.45 & ~ ( Xphi @ Xx ) )
% 2.34/1.45 => ~ ! [Xx: $i] :
% 2.34/1.45 ( ( in @ Xx @ A )
% 2.34/1.45 => ( Xphi @ Xx ) ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(prop2setI_type,type,
% 2.34/1.45 prop2setI: $o ).
% 2.34/1.45
% 2.34/1.45 thf(prop2setI,definition,
% 2.34/1.45 ( prop2setI
% 2.34/1.45 = ( ! [Xphi: $o] :
% 2.34/1.45 ( Xphi
% 2.34/1.45 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(set2prop_type,type,
% 2.34/1.45 set2prop: $i > $o ).
% 2.34/1.45
% 2.34/1.45 thf(prop2set2propI_type,type,
% 2.34/1.45 prop2set2propI: $o ).
% 2.34/1.45
% 2.34/1.45 thf(prop2set2propI,definition,
% 2.34/1.45 ( prop2set2propI
% 2.34/1.45 = ( ! [Xphi: $o] :
% 2.34/1.45 ( Xphi
% 2.34/1.45 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(notdexE_type,type,
% 2.34/1.45 notdexE: $o ).
% 2.34/1.45
% 2.34/1.45 thf(notdexE,definition,
% 2.34/1.45 ( notdexE
% 2.34/1.45 = ( ! [A: $i,Xphi: $i > $o] :
% 2.34/1.45 ( ~ ? [Xx: $i] :
% 2.34/1.45 ( ( in @ Xx @ A )
% 2.34/1.45 & ( Xphi @ Xx ) )
% 2.34/1.45 => ! [Xx: $i] :
% 2.34/1.45 ( ( in @ Xx @ A )
% 2.34/1.45 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(notdallE_type,type,
% 2.34/1.45 notdallE: $o ).
% 2.34/1.45
% 2.34/1.45 thf(notdallE,definition,
% 2.34/1.45 ( notdallE
% 2.34/1.45 = ( ! [A: $i,Xphi: $i > $o] :
% 2.34/1.45 ( ~ ! [Xx: $i] :
% 2.34/1.45 ( ( in @ Xx @ A )
% 2.34/1.45 => ( Xphi @ Xx ) )
% 2.34/1.45 => ? [Xx: $i] :
% 2.34/1.45 ( ( in @ Xx @ A )
% 2.34/1.45 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(exuI1_type,type,
% 2.34/1.45 exuI1: $o ).
% 2.34/1.45
% 2.34/1.45 thf(exuI1,definition,
% 2.34/1.45 ( exuI1
% 2.34/1.45 = ( ! [Xphi: $i > $o] :
% 2.34/1.45 ( ? [Xx: $i] :
% 2.34/1.45 ( ( Xphi @ Xx )
% 2.34/1.45 & ! [Xy: $i] :
% 2.34/1.45 ( ( Xphi @ Xy )
% 2.34/1.45 => ( Xx = Xy ) ) )
% 2.34/1.45 => ( exu
% 2.34/1.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(exuI3_type,type,
% 2.34/1.45 exuI3: $o ).
% 2.34/1.45
% 2.34/1.45 thf(exuI3,definition,
% 2.34/1.45 ( exuI3
% 2.34/1.45 = ( ! [Xphi: $i > $o] :
% 2.34/1.45 ( ? [Xx: $i] : ( Xphi @ Xx )
% 2.34/1.45 => ( ! [Xx: $i,Xy: $i] :
% 2.34/1.45 ( ( Xphi @ Xx )
% 2.34/1.45 => ( ( Xphi @ Xy )
% 2.34/1.45 => ( Xx = Xy ) ) )
% 2.34/1.45 => ( exu
% 2.34/1.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(exuI2_type,type,
% 2.34/1.45 exuI2: $o ).
% 2.34/1.45
% 2.34/1.45 thf(exuI2,definition,
% 2.34/1.45 ( exuI2
% 2.34/1.45 = ( ! [Xphi: $i > $o] :
% 2.34/1.45 ( ? [Xx: $i] :
% 2.34/1.45 ! [Xy: $i] :
% 2.34/1.45 ( ( Xphi @ Xy )
% 2.34/1.45 <=> ( Xy = Xx ) )
% 2.34/1.45 => ( exu
% 2.34/1.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(inCongP_type,type,
% 2.34/1.45 inCongP: $o ).
% 2.34/1.45
% 2.34/1.45 thf(inCongP,definition,
% 2.34/1.45 ( inCongP
% 2.34/1.45 = ( ! [A: $i,B: $i] :
% 2.34/1.45 ( ( A = B )
% 2.34/1.45 => ! [Xx: $i,Xy: $i] :
% 2.34/1.45 ( ( Xx = Xy )
% 2.34/1.45 => ( ( in @ Xx @ A )
% 2.34/1.45 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(in__Cong_type,type,
% 2.34/1.45 in__Cong: $o ).
% 2.34/1.45
% 2.34/1.45 thf(in__Cong,definition,
% 2.34/1.45 ( in__Cong
% 2.34/1.45 = ( ! [A: $i,B: $i] :
% 2.34/1.45 ( ( A = B )
% 2.34/1.45 => ! [Xx: $i,Xy: $i] :
% 2.34/1.45 ( ( Xx = Xy )
% 2.34/1.45 => ( ( in @ Xx @ A )
% 2.34/1.45 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(exuE3u_type,type,
% 2.34/1.45 exuE3u: $o ).
% 2.34/1.45
% 2.34/1.45 thf(exuE3u,definition,
% 2.34/1.45 ( exuE3u
% 2.34/1.45 = ( ! [Xphi: $i > $o] :
% 2.34/1.45 ( ( exu
% 2.34/1.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.34/1.45 => ! [Xx: $i,Xy: $i] :
% 2.34/1.45 ( ( Xphi @ Xx )
% 2.34/1.45 => ( ( Xphi @ Xy )
% 2.34/1.45 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(exu__Cong_type,type,
% 2.34/1.45 exu__Cong: $o ).
% 2.34/1.45
% 2.34/1.45 thf(exu__Cong,definition,
% 2.34/1.45 ( exu__Cong
% 2.34/1.45 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.34/1.45 ( ! [Xx: $i,Xy: $i] :
% 2.34/1.45 ( ( Xx = Xy )
% 2.34/1.45 => ( ( Xphi @ Xx )
% 2.34/1.45 <=> ( Xpsi @ Xy ) ) )
% 2.34/1.45 => ( ( exu
% 2.34/1.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.34/1.45 <=> ( exu
% 2.34/1.45 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(emptyset__Cong_type,type,
% 2.34/1.45 emptyset__Cong: $o ).
% 2.34/1.45
% 2.34/1.45 thf(emptyset__Cong,definition,
% 2.34/1.45 ( emptyset__Cong
% 2.34/1.45 = ( emptyset = emptyset ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(setadjoin__Cong_type,type,
% 2.34/1.45 setadjoin__Cong: $o ).
% 2.34/1.45
% 2.34/1.45 thf(setadjoin__Cong,definition,
% 2.34/1.45 ( setadjoin__Cong
% 2.34/1.45 = ( ! [Xx: $i,Xy: $i] :
% 2.34/1.45 ( ( Xx = Xy )
% 2.34/1.45 => ! [Xz: $i,Xu: $i] :
% 2.34/1.45 ( ( Xz = Xu )
% 2.34/1.45 => ( ( setadjoin @ Xx @ Xz )
% 2.34/1.45 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(powerset__Cong_type,type,
% 2.34/1.45 powerset__Cong: $o ).
% 2.34/1.45
% 2.34/1.45 thf(powerset__Cong,definition,
% 2.34/1.45 ( powerset__Cong
% 2.34/1.45 = ( ! [A: $i,B: $i] :
% 2.34/1.45 ( ( A = B )
% 2.34/1.45 => ( ( powerset @ A )
% 2.34/1.45 = ( powerset @ B ) ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(setunion__Cong_type,type,
% 2.34/1.45 setunion__Cong: $o ).
% 2.34/1.45
% 2.34/1.45 thf(setunion__Cong,definition,
% 2.34/1.45 ( setunion__Cong
% 2.34/1.45 = ( ! [A: $i,B: $i] :
% 2.34/1.45 ( ( A = B )
% 2.34/1.45 => ( ( setunion @ A )
% 2.34/1.45 = ( setunion @ B ) ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(omega__Cong_type,type,
% 2.34/1.45 omega__Cong: $o ).
% 2.34/1.45
% 2.34/1.45 thf(omega__Cong,definition,
% 2.34/1.45 ( omega__Cong
% 2.34/1.45 = ( omega = omega ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(exuEu_type,type,
% 2.34/1.45 exuEu: $o ).
% 2.34/1.45
% 2.34/1.45 thf(exuEu,definition,
% 2.34/1.45 ( exuEu
% 2.34/1.45 = ( ! [Xphi: $i > $o] :
% 2.34/1.45 ( ( exu
% 2.34/1.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.34/1.45 => ! [Xx: $i,Xy: $i] :
% 2.34/1.45 ( ( Xphi @ Xx )
% 2.34/1.45 => ( ( Xphi @ Xy )
% 2.34/1.45 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(descr__Cong_type,type,
% 2.34/1.45 descr__Cong: $o ).
% 2.34/1.45
% 2.34/1.45 thf(descr__Cong,definition,
% 2.34/1.45 ( descr__Cong
% 2.34/1.45 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.34/1.45 ( ! [Xx: $i,Xy: $i] :
% 2.34/1.45 ( ( Xx = Xy )
% 2.34/1.45 => ( ( Xphi @ Xx )
% 2.34/1.45 <=> ( Xpsi @ Xy ) ) )
% 2.34/1.45 => ( ( exu
% 2.34/1.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.34/1.45 => ( ( exu
% 2.34/1.45 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 2.34/1.45 => ( ( descr
% 2.34/1.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.34/1.45 = ( descr
% 2.34/1.45 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(dsetconstr__Cong_type,type,
% 2.34/1.45 dsetconstr__Cong: $o ).
% 2.34/1.45
% 2.34/1.45 thf(dsetconstr__Cong,definition,
% 2.34/1.45 ( dsetconstr__Cong
% 2.34/1.45 = ( ! [A: $i,B: $i] :
% 2.34/1.45 ( ( A = B )
% 2.34/1.45 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.34/1.45 ( ! [Xx: $i] :
% 2.34/1.45 ( ( in @ Xx @ A )
% 2.34/1.45 => ! [Xy: $i] :
% 2.34/1.45 ( ( in @ Xy @ B )
% 2.34/1.45 => ( ( Xx = Xy )
% 2.34/1.45 => ( ( Xphi @ Xx )
% 2.34/1.45 <=> ( Xpsi @ Xy ) ) ) ) )
% 2.34/1.45 => ( ( dsetconstr @ A
% 2.34/1.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.34/1.45 = ( dsetconstr @ B
% 2.34/1.45 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(subset_type,type,
% 2.34/1.45 subset: $i > $i > $o ).
% 2.34/1.45
% 2.34/1.45 thf(disjoint_type,type,
% 2.34/1.45 disjoint: $i > $i > $o ).
% 2.34/1.45
% 2.34/1.45 thf(setsmeet_type,type,
% 2.34/1.45 setsmeet: $i > $i > $o ).
% 2.34/1.45
% 2.34/1.45 thf(subsetI1_type,type,
% 2.34/1.45 subsetI1: $o ).
% 2.34/1.45
% 2.34/1.45 thf(subsetI1,definition,
% 2.34/1.45 ( subsetI1
% 2.34/1.45 = ( ! [A: $i,B: $i] :
% 2.34/1.45 ( ! [Xx: $i] :
% 2.34/1.45 ( ( in @ Xx @ A )
% 2.34/1.45 => ( in @ Xx @ B ) )
% 2.34/1.45 => ( subset @ A @ B ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(eqimpsubset2_type,type,
% 2.34/1.45 eqimpsubset2: $o ).
% 2.34/1.45
% 2.34/1.45 thf(eqimpsubset2,definition,
% 2.34/1.45 ( eqimpsubset2
% 2.34/1.45 = ( ! [A: $i,B: $i] :
% 2.34/1.45 ( ( A = B )
% 2.34/1.45 => ( subset @ B @ A ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(eqimpsubset1_type,type,
% 2.34/1.45 eqimpsubset1: $o ).
% 2.34/1.45
% 2.34/1.45 thf(eqimpsubset1,definition,
% 2.34/1.45 ( eqimpsubset1
% 2.34/1.45 = ( ! [A: $i,B: $i] :
% 2.34/1.45 ( ( A = B )
% 2.34/1.45 => ( subset @ A @ B ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(subsetI2_type,type,
% 2.34/1.45 subsetI2: $o ).
% 2.34/1.45
% 2.34/1.45 thf(subsetI2,definition,
% 2.34/1.45 ( subsetI2
% 2.34/1.45 = ( ! [A: $i,B: $i] :
% 2.34/1.45 ( ! [Xx: $i] :
% 2.34/1.45 ( ( in @ Xx @ A )
% 2.34/1.45 => ( in @ Xx @ B ) )
% 2.34/1.45 => ( subset @ A @ B ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(emptysetsubset_type,type,
% 2.34/1.45 emptysetsubset: $o ).
% 2.34/1.45
% 2.34/1.45 thf(emptysetsubset,definition,
% 2.34/1.45 ( emptysetsubset
% 2.34/1.45 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(subsetE_type,type,
% 2.34/1.45 subsetE: $o ).
% 2.34/1.45
% 2.34/1.45 thf(subsetE,definition,
% 2.34/1.45 ( subsetE
% 2.34/1.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.34/1.45 ( ( subset @ A @ B )
% 2.34/1.45 => ( ( in @ Xx @ A )
% 2.34/1.45 => ( in @ Xx @ B ) ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(subsetE2,conjecture,
% 2.34/1.45 ( setextAx
% 2.34/1.45 => ( emptysetAx
% 2.34/1.45 => ( setadjoinAx
% 2.34/1.45 => ( powersetAx
% 2.34/1.45 => ( setunionAx
% 2.34/1.45 => ( omega0Ax
% 2.34/1.45 => ( omegaSAx
% 2.34/1.45 => ( omegaIndAx
% 2.34/1.45 => ( replAx
% 2.34/1.45 => ( foundationAx
% 2.34/1.45 => ( wellorderingAx
% 2.34/1.45 => ( descrp
% 2.34/1.45 => ( dsetconstrI
% 2.34/1.45 => ( dsetconstrEL
% 2.34/1.45 => ( dsetconstrER
% 2.34/1.45 => ( exuE1
% 2.34/1.45 => ( prop2setE
% 2.34/1.45 => ( emptysetE
% 2.34/1.45 => ( emptysetimpfalse
% 2.34/1.45 => ( notinemptyset
% 2.34/1.45 => ( exuE3e
% 2.34/1.45 => ( setext
% 2.34/1.45 => ( emptyI
% 2.34/1.45 => ( noeltsimpempty
% 2.34/1.45 => ( setbeta
% 2.34/1.45 => ( nonemptyE1
% 2.34/1.45 => ( nonemptyI
% 2.34/1.45 => ( nonemptyI1
% 2.34/1.45 => ( setadjoinIL
% 2.34/1.45 => ( emptyinunitempty
% 2.34/1.45 => ( setadjoinIR
% 2.34/1.45 => ( setadjoinE
% 2.34/1.45 => ( setadjoinOr
% 2.34/1.45 => ( setoftrueEq
% 2.34/1.45 => ( powersetI
% 2.34/1.45 => ( emptyinPowerset
% 2.34/1.45 => ( emptyInPowerset
% 2.34/1.45 => ( powersetE
% 2.34/1.45 => ( setunionI
% 2.34/1.45 => ( setunionE
% 2.34/1.45 => ( subPowSU
% 2.34/1.45 => ( exuE2
% 2.34/1.45 => ( nonemptyImpWitness
% 2.34/1.45 => ( uniqinunit
% 2.34/1.45 => ( notinsingleton
% 2.34/1.45 => ( eqinunit
% 2.34/1.45 => ( singletonsswitch
% 2.34/1.45 => ( upairsetE
% 2.34/1.45 => ( upairsetIL
% 2.34/1.45 => ( upairsetIR
% 2.34/1.45 => ( emptyE1
% 2.34/1.45 => ( vacuousDall
% 2.34/1.45 => ( quantDeMorgan1
% 2.34/1.45 => ( quantDeMorgan2
% 2.34/1.45 => ( quantDeMorgan3
% 2.34/1.45 => ( quantDeMorgan4
% 2.34/1.45 => ( prop2setI
% 2.34/1.45 => ( prop2set2propI
% 2.34/1.45 => ( notdexE
% 2.34/1.45 => ( notdallE
% 2.34/1.45 => ( exuI1
% 2.34/1.45 => ( exuI3
% 2.34/1.45 => ( exuI2
% 2.34/1.45 => ( inCongP
% 2.34/1.45 => ( in__Cong
% 2.34/1.45 => ( exuE3u
% 2.34/1.45 => ( exu__Cong
% 2.34/1.45 => ( emptyset__Cong
% 2.34/1.45 => ( setadjoin__Cong
% 2.34/1.45 => ( powerset__Cong
% 2.34/1.45 => ( setunion__Cong
% 2.34/1.45 => ( omega__Cong
% 2.34/1.45 => ( exuEu
% 2.34/1.45 => ( descr__Cong
% 2.34/1.45 => ( dsetconstr__Cong
% 2.34/1.45 => ( subsetI1
% 2.34/1.45 => ( eqimpsubset2
% 2.34/1.45 => ( eqimpsubset1
% 2.34/1.45 => ( subsetI2
% 2.34/1.45 => ( emptysetsubset
% 2.34/1.45 => ( subsetE
% 2.34/1.45 => ! [A: $i,B: $i,Xx: $i] :
% 2.34/1.45 ( ( subset @ A @ B )
% 2.34/1.45 => ( ~ ( in @ Xx @ B )
% 2.34/1.45 => ~ ( in @ Xx @ A ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.34/1.45 ------------------------
% 2.34/1.47 % (26301)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_26070 for (2999ds/2Mi)
% 2.34/1.47 % (26299)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_26070 for (2999ds/2Mi)
% 2.34/1.47 % (26299)Instruction limit reached!
% 2.34/1.47 % (26299)------------------------------
% 2.34/1.47 % (26299)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.34/1.47 % (26299)Termination reason: Unknown
% 2.34/1.47 % (26299)Termination phase: shuffling
% 2.34/1.47
% 2.34/1.47 % (26299)Memory used [KB]: 1151
% 2.34/1.47 % (26299)Time elapsed: 0.002 s
% 2.34/1.47 % (26299)Instructions burned: 2 (million)
% 2.34/1.47 % (26299)------------------------------
% 2.34/1.47 % (26299)------------------------------
% 2.34/1.47 % (26301)Instruction limit reached!
% 2.34/1.47 % (26301)------------------------------
% 2.34/1.47 % (26301)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.34/1.47 % (26301)Termination reason: Unknown
% 2.34/1.47 % (26301)Termination phase: shuffling
% 2.34/1.47
% 2.34/1.47 % (26301)Memory used [KB]: 1151
% 2.34/1.47 % (26301)Time elapsed: 0.003 s
% 2.34/1.47 % (26301)Instructions burned: 5 (million)
% 2.34/1.47 % (26301)------------------------------
% 2.34/1.47 % (26301)------------------------------
% 2.34/1.48 % (26296)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_26070 for (2999ds/183Mi)
% 2.34/1.48 % (26298)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_26070 for (2999ds/27Mi)
% 2.34/1.48 % (26297)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_26070 for (2999ds/4Mi)
% 2.34/1.48 % (26304)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_26070 for (2999ds/18Mi)
% 2.34/1.48 % (26302)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_26070 for (2999ds/275Mi)
% 2.34/1.48 % (26297)Instruction limit reached!
% 2.34/1.48 % (26297)------------------------------
% 2.34/1.48 % (26297)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.34/1.48 % (26297)Termination reason: Unknown
% 2.34/1.48 % (26297)Termination phase: shuffling
% 2.34/1.48
% 2.34/1.48 % (26297)Memory used [KB]: 1151
% 2.34/1.48 % (26297)Time elapsed: 0.005 s
% 2.34/1.48 % (26297)Instructions burned: 5 (million)
% 2.34/1.48 % (26297)------------------------------
% 2.34/1.48 % (26297)------------------------------
% 2.34/1.48 % (26314)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_26070 for (2999ds/37Mi)
% 2.34/1.48 % (26313)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_26070 for (2999ds/3Mi)
% 2.34/1.48 % (26313)Instruction limit reached!
% 2.34/1.48 % (26313)------------------------------
% 2.34/1.48 % (26313)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.34/1.48 % (26313)Termination reason: Unknown
% 2.34/1.48 % (26313)Termination phase: shuffling
% 2.34/1.48
% 2.34/1.48 % (26313)Memory used [KB]: 1151
% 2.34/1.48 % (26313)Time elapsed: 0.003 s
% 2.34/1.48 % (26313)Instructions burned: 4 (million)
% 2.34/1.48 % (26313)------------------------------
% 2.34/1.48 % (26313)------------------------------
% 2.34/1.49 % (26304)Instruction limit reached!
% 2.34/1.49 % (26304)------------------------------
% 2.34/1.49 % (26304)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.34/1.49 % (26304)Termination reason: Unknown
% 2.34/1.49 % (26304)Termination phase: Preprocessing 3
% 2.34/1.49
% 2.34/1.49 % (26304)Memory used [KB]: 1535
% 2.34/1.49 % (26304)Time elapsed: 0.012 s
% 2.34/1.49 % (26304)Instructions burned: 18 (million)
% 2.34/1.49 % (26304)------------------------------
% 2.34/1.49 % (26304)------------------------------
% 2.34/1.49 % (26298)Instruction limit reached!
% 2.34/1.49 % (26298)------------------------------
% 2.34/1.49 % (26298)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.34/1.49 % (26298)Termination reason: Unknown
% 2.34/1.49 % (26298)Termination phase: Property scanning
% 2.34/1.49
% 2.34/1.49 % (26298)Memory used [KB]: 1407
% 2.34/1.49 % (26298)Time elapsed: 0.014 s
% 2.34/1.49 % (26298)Instructions burned: 27 (million)
% 2.34/1.49 % (26298)------------------------------
% 2.34/1.49 % (26298)------------------------------
% 2.34/1.49 % (26314)Instruction limit reached!
% 2.34/1.49 % (26314)------------------------------
% 2.34/1.49 % (26314)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.34/1.49 % (26314)Termination reason: Unknown
% 2.34/1.49 % (26314)Termination phase: Property scanning
% 2.34/1.49
% 2.34/1.49 % (26314)Memory used [KB]: 1407
% 2.34/1.49 % (26314)Time elapsed: 0.011 s
% 2.34/1.49 % (26314)Instructions burned: 40 (million)
% 2.34/1.49 % (26314)------------------------------
% 2.34/1.49 % (26314)------------------------------
% 2.34/1.49 % (26323)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_26070 for (2999ds/3Mi)
% 2.34/1.49 % (26323)Instruction limit reached!
% 2.34/1.49 % (26323)------------------------------
% 2.34/1.49 % (26323)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.34/1.49 % (26323)Termination reason: Unknown
% 2.34/1.49 % (26323)Termination phase: shuffling
% 2.34/1.49
% 2.34/1.49 % (26323)Memory used [KB]: 1151
% 2.34/1.49 % (26323)Time elapsed: 0.003 s
% 2.34/1.49 % (26323)Instructions burned: 4 (million)
% 2.34/1.49 % (26323)------------------------------
% 2.34/1.49 % (26323)------------------------------
% 2.43/1.50 % (26321)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_26070 for (2999ds/15Mi)
% 2.43/1.50 % (26327)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_26070 for (2999ds/16Mi)
% 2.43/1.50 % (26326)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_26070 for (2999ds/7Mi)
% 2.43/1.50 % (26325)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_26070 for (2999ds/1041Mi)
% 2.43/1.50 % (26328)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_26070 for (2999ds/3Mi)
% 2.43/1.50 % (26326)Instruction limit reached!
% 2.43/1.50 % (26326)------------------------------
% 2.43/1.50 % (26326)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.43/1.50 % (26326)Termination reason: Unknown
% 2.43/1.50 % (26326)Termination phase: shuffling
% 2.43/1.50
% 2.43/1.50 % (26326)Memory used [KB]: 1279
% 2.43/1.50 % (26326)Time elapsed: 0.004 s
% 2.43/1.50 % (26326)Instructions burned: 9 (million)
% 2.43/1.50 % (26326)------------------------------
% 2.43/1.50 % (26326)------------------------------
% 2.43/1.50 % (26327)Instruction limit reached!
% 2.43/1.50 % (26327)------------------------------
% 2.43/1.50 % (26327)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.43/1.50 % (26327)Termination reason: Unknown
% 2.43/1.50 % (26327)Termination phase: Property scanning
% 2.43/1.50
% 2.43/1.50 % (26327)Memory used [KB]: 1407
% 2.43/1.50 % (26327)Time elapsed: 0.006 s
% 2.43/1.50 % (26327)Instructions burned: 18 (million)
% 2.43/1.50 % (26327)------------------------------
% 2.43/1.50 % (26327)------------------------------
% 2.43/1.51 % (26328)Instruction limit reached!
% 2.43/1.51 % (26328)------------------------------
% 2.43/1.51 % (26328)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.43/1.51 % (26328)Termination reason: Unknown
% 2.43/1.51 % (26328)Termination phase: shuffling
% 2.43/1.51
% 2.43/1.51 % (26328)Memory used [KB]: 1151
% 2.43/1.51 % (26328)Time elapsed: 0.002 s
% 2.43/1.51 % (26328)Instructions burned: 4 (million)
% 2.43/1.51 % (26328)------------------------------
% 2.43/1.51 % (26328)------------------------------
% 2.43/1.51 % (26321)Instruction limit reached!
% 2.43/1.51 % (26321)------------------------------
% 2.43/1.51 % (26321)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.43/1.51 % (26321)Termination reason: Unknown
% 2.43/1.51 % (26321)Termination phase: Preprocessing 3
% 2.43/1.51
% 2.43/1.51 % (26321)Memory used [KB]: 1535
% 2.43/1.51 % (26321)Time elapsed: 0.011 s
% 2.43/1.51 % (26321)Instructions burned: 16 (million)
% 2.43/1.51 % (26321)------------------------------
% 2.43/1.51 % (26321)------------------------------
% 2.43/1.51 % (26338)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_26070 for (2999ds/7Mi)
% 2.43/1.51 % (26336)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_26070 for (2999ds/3Mi)
% 2.43/1.52 % (26339)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_26070 for (2999ds/3Mi)
% 2.43/1.52 % (26336)Instruction limit reached!
% 2.43/1.52 % (26336)------------------------------
% 2.43/1.52 % (26336)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.43/1.52 % (26336)Termination reason: Unknown
% 2.43/1.52 % (26336)Termination phase: shuffling
% 2.43/1.52
% 2.43/1.52 % (26336)Memory used [KB]: 1151
% 2.43/1.52 % (26336)Time elapsed: 0.003 s
% 2.43/1.52 % (26336)Instructions burned: 4 (million)
% 2.43/1.52 % (26336)------------------------------
% 2.43/1.52 % (26336)------------------------------
% 2.43/1.52 % (26338)Instruction limit reached!
% 2.43/1.52 % (26338)------------------------------
% 2.43/1.52 % (26338)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.43/1.52 % (26338)Termination reason: Unknown
% 2.43/1.52 % (26338)Termination phase: shuffling
% 2.43/1.52
% 2.43/1.52 % (26338)Memory used [KB]: 1279
% 2.43/1.52 % (26338)Time elapsed: 0.003 s
% 2.43/1.52 % (26338)Instructions burned: 8 (million)
% 2.43/1.52 % (26338)------------------------------
% 2.43/1.52 % (26338)------------------------------
% 2.43/1.52 % (26339)Instruction limit reached!
% 2.43/1.52 % (26339)------------------------------
% 2.43/1.52 % (26339)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.43/1.52 % (26339)Termination reason: Unknown
% 2.43/1.52 % (26339)Termination phase: shuffling
% 2.43/1.52
% 2.43/1.52 % (26339)Memory used [KB]: 1151
% 2.43/1.52 % (26339)Time elapsed: 0.003 s
% 2.43/1.52 % (26339)Instructions burned: 4 (million)
% 2.43/1.52 % (26339)------------------------------
% 2.43/1.52 % (26339)------------------------------
% 2.43/1.52 % (26341)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_26070 for (2999ds/4Mi)
% 2.43/1.52 % (26341)Instruction limit reached!
% 2.43/1.52 % (26341)------------------------------
% 2.43/1.52 % (26341)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.43/1.52 % (26341)Termination reason: Unknown
% 2.43/1.52 % (26341)Termination phase: shuffling
% 2.43/1.52
% 2.43/1.52 % (26341)Memory used [KB]: 1151
% 2.43/1.52 % (26341)Time elapsed: 0.003 s
% 2.43/1.52 % (26341)Instructions burned: 4 (million)
% 2.43/1.52 % (26341)------------------------------
% 2.43/1.52 % (26341)------------------------------
% 2.43/1.53 % (26348)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_26070 for (2999ds/18Mi)
% 2.43/1.53 % (26351)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_26070 for (2999ds/6Mi)
% 2.43/1.53 % (26351)Instruction limit reached!
% 2.43/1.53 % (26351)------------------------------
% 2.43/1.53 % (26351)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.43/1.53 % (26351)Termination reason: Unknown
% 2.43/1.53 % (26351)Termination phase: shuffling
% 2.43/1.53
% 2.43/1.53 % (26351)Memory used [KB]: 1279
% 2.43/1.53 % (26351)Time elapsed: 0.004 s
% 2.43/1.53 % (26351)Instructions burned: 8 (million)
% 2.43/1.53 % (26351)------------------------------
% 2.43/1.53 % (26351)------------------------------
% 2.43/1.53 % (26348)Instruction limit reached!
% 2.43/1.53 % (26348)------------------------------
% 2.43/1.53 % (26348)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.43/1.53 % (26348)Termination reason: Unknown
% 2.43/1.53 % (26348)Termination phase: Property scanning
% 2.43/1.53
% 2.43/1.53 % (26348)Memory used [KB]: 1407
% 2.43/1.53 % (26348)Time elapsed: 0.007 s
% 2.43/1.53 % (26348)Instructions burned: 18 (million)
% 2.43/1.53 % (26348)------------------------------
% 2.43/1.53 % (26348)------------------------------
% 2.43/1.53 % (26350)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_26070 for (2999ds/710Mi)
% 2.43/1.54 % (26355)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_26070 for (2999ds/902Mi)
% 2.43/1.54 % (26361)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_26070 for (2999ds/21Mi)
% 2.43/1.54 % (26296)Instruction limit reached!
% 2.43/1.54 % (26296)------------------------------
% 2.43/1.54 % (26296)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.43/1.54 % (26296)Termination reason: Unknown
% 2.43/1.54 % (26296)Termination phase: Saturation
% 2.43/1.54
% 2.43/1.54 % (26296)Memory used [KB]: 6780
% 2.43/1.54 % (26296)Time elapsed: 0.065 s
% 2.43/1.54 % (26296)Instructions burned: 184 (million)
% 2.43/1.54 % (26296)------------------------------
% 2.43/1.54 % (26296)------------------------------
% 2.43/1.54 % (26362)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_26070 for (2999ds/5Mi)
% 2.43/1.54 % (26362)Instruction limit reached!
% 2.43/1.54 % (26362)------------------------------
% 2.43/1.54 % (26362)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.43/1.54 % (26362)Termination reason: Unknown
% 2.43/1.54 % (26362)Termination phase: shuffling
% 2.43/1.54
% 2.43/1.54 % (26362)Memory used [KB]: 1279
% 2.43/1.54 % (26362)Time elapsed: 0.004 s
% 2.43/1.54 % (26362)Instructions burned: 8 (million)
% 2.43/1.54 % (26362)------------------------------
% 2.43/1.54 % (26362)------------------------------
% 2.43/1.55 % (26361)Instruction limit reached!
% 2.43/1.55 % (26361)------------------------------
% 2.43/1.55 % (26361)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.43/1.55 % (26361)Termination reason: Unknown
% 2.43/1.55 % (26361)Termination phase: SInE selection
% 2.43/1.55
% 2.43/1.55 % (26361)Memory used [KB]: 1407
% 2.43/1.55 % (26361)Time elapsed: 0.008 s
% 2.43/1.55 % (26361)Instructions burned: 22 (million)
% 2.43/1.55 % (26361)------------------------------
% 2.43/1.55 % (26361)------------------------------
% 2.43/1.55 % (26363)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_26070 for (2999ds/6Mi)
% 2.43/1.55 % (26363)Instruction limit reached!
% 2.43/1.55 % (26363)------------------------------
% 2.43/1.55 % (26363)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.43/1.55 % (26363)Termination reason: Unknown
% 2.43/1.55 % (26363)Termination phase: shuffling
% 2.43/1.55
% 2.43/1.55 % (26363)Memory used [KB]: 1279
% 2.43/1.55 % (26363)Time elapsed: 0.003 s
% 2.43/1.55 % (26363)Instructions burned: 8 (million)
% 2.43/1.55 % (26363)------------------------------
% 2.43/1.55 % (26363)------------------------------
% 2.43/1.55 % (26364)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_26070 for (2999ds/377Mi)
% 2.43/1.56 % (26366)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_26070 for (2999ds/779Mi)
% 2.43/1.56 % (26375)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_26070 for (2999ds/19Mi)
% 2.43/1.57 % (26375)Instruction limit reached!
% 2.43/1.57 % (26375)------------------------------
% 2.43/1.57 % (26375)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.43/1.57 % (26375)Termination reason: Unknown
% 2.43/1.57 % (26375)Termination phase: Property scanning
% 2.43/1.57
% 2.43/1.57 % (26375)Memory used [KB]: 1407
% 2.43/1.57 % (26375)Time elapsed: 0.007 s
% 2.43/1.57 % (26375)Instructions burned: 19 (million)
% 2.43/1.57 % (26375)------------------------------
% 2.43/1.57 % (26375)------------------------------
% 2.43/1.58 % (26382)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_26070 for (2998ds/879Mi)
% 2.43/1.58 % (26355)First to succeed.
% 2.43/1.58 % (26355)Refutation found. Thanks to Tanya!
% 2.43/1.58 % SZS status Theorem for DTF2THF_26070
% 2.43/1.58 % SZS output start Proof for DTF2THF_26070
% 2.43/1.58 thf(func_def_0, type, in: $i > $i > $o).
% 2.43/1.58 thf(func_def_1, type, exu: ($i > $o) > $o).
% 2.43/1.58 thf(func_def_6, type, setadjoin: $i > $i > $i).
% 2.43/1.58 thf(func_def_8, type, powerset: $i > $i).
% 2.43/1.58 thf(func_def_10, type, setunion: $i > $i).
% 2.43/1.58 thf(func_def_19, type, descr: ($i > $o) > $i).
% 2.43/1.58 thf(func_def_21, type, dsetconstr: $i > ($i > $o) > $i).
% 2.43/1.58 thf(func_def_26, type, prop2set: $o > $i).
% 2.43/1.58 thf(func_def_36, type, nonempty: $i > $o).
% 2.43/1.58 thf(func_def_69, type, set2prop: $i > $o).
% 2.43/1.58 thf(func_def_88, type, subset: $i > $i > $o).
% 2.43/1.58 thf(func_def_89, type, disjoint: $i > $i > $o).
% 2.43/1.58 thf(func_def_90, type, setsmeet: $i > $i > $o).
% 2.43/1.58 thf(func_def_110, type, sP1: $i > $i > $o).
% 2.43/1.58 thf(func_def_111, type, sP2: $i > $o).
% 2.43/1.58 thf(func_def_112, type, sP3: $i > $i > $o).
% 2.43/1.58 thf(func_def_113, type, sP4: $i > $i > $o).
% 2.43/1.58 thf(func_def_115, type, sK6: $i > $i).
% 2.43/1.58 thf(func_def_118, type, sK9: $i > $o).
% 2.43/1.58 thf(func_def_121, type, sK12: $i > $i > $o).
% 2.43/1.58 thf(func_def_122, type, sK13: $i > $i).
% 2.43/1.58 thf(func_def_123, type, sK14: $i > $i).
% 2.43/1.58 thf(func_def_124, type, sK15: ($i > $i > $o) > $i > $i).
% 2.43/1.58 thf(func_def_125, type, sK16: ($i > $i > $o) > $i > $i).
% 2.43/1.58 thf(func_def_126, type, sK17: $i > ($i > $i > $o) > $i > $i).
% 2.43/1.58 thf(func_def_127, type, sK18: $i > $o).
% 2.43/1.58 thf(func_def_128, type, sK19: ($i > $o) > ($i > $o) > $i > $i > $i).
% 2.43/1.58 thf(func_def_129, type, sK20: ($i > $o) > ($i > $o) > $i > $i > $i).
% 2.43/1.58 thf(func_def_132, type, sK23: $i > $o).
% 2.43/1.58 thf(func_def_133, type, sK24: $i > $o).
% 2.43/1.58 thf(func_def_140, type, sK31: $i > $i > $i).
% 2.43/1.58 thf(func_def_142, type, sK33: $i > $i).
% 2.43/1.58 thf(func_def_146, type, sK37: ($i > $o) > ($i > $o) > $i).
% 2.43/1.58 thf(func_def_147, type, sK38: ($i > $o) > ($i > $o) > $i).
% 2.43/1.58 thf(func_def_148, type, sK39: $i > $o).
% 2.43/1.58 thf(func_def_149, type, sK40: $i > $o).
% 2.43/1.58 thf(func_def_156, type, sK47: $i > $i).
% 2.43/1.58 thf(func_def_162, type, sK53: ($i > $o) > $i).
% 2.43/1.58 thf(func_def_163, type, sK54: $i > $o).
% 2.43/1.58 thf(func_def_171, type, sK62: ($i > $o) > $i).
% 2.43/1.58 thf(func_def_172, type, sK63: $i > $o).
% 2.43/1.58 thf(func_def_173, type, sK64: $i > $i).
% 2.43/1.58 thf(func_def_174, type, sK65: $i > $o).
% 2.43/1.58 thf(func_def_178, type, sK69: $i > $i > $i).
% 2.43/1.58 thf(func_def_184, type, sK75: $i > $o).
% 2.43/1.58 thf(func_def_185, type, sK76: $i > ($i > $o) > $i).
% 2.43/1.58 thf(func_def_186, type, sK77: $i > $o).
% 2.43/1.58 thf(func_def_189, type, sK80: $i > $i > $i).
% 2.43/1.58 thf(func_def_190, type, sK81: $i > $i > $i).
% 2.43/1.58 thf(func_def_193, type, sK84: $i > $o).
% 2.43/1.58 thf(func_def_195, type, sK86: $i > ($i > $o) > $i).
% 2.43/1.58 thf(func_def_205, type, sK96: $i > $i).
% 2.43/1.58 thf(func_def_207, type, sK98: $i > $i).
% 2.43/1.58 thf(func_def_208, type, sK99: $i > $i > $i).
% 2.43/1.58 thf(func_def_213, type, sK104: $i > $i > $i).
% 2.43/1.58 thf(func_def_220, type, sK111: $i > $o).
% 2.43/1.58 thf(func_def_226, type, sK117: $i > $o).
% 2.43/1.58 thf(func_def_228, type, sK119: ($i > $o) > $i > $i).
% 2.43/1.58 thf(func_def_231, type, sK122: $i > $o).
% 2.43/1.58 thf(func_def_232, type, sK123: $i > $i).
% 2.43/1.58 thf(func_def_233, type, sK124: ($i > $o) > $i).
% 2.43/1.58 thf(func_def_237, type, sK128: $i > $o).
% 2.43/1.58 thf(func_def_242, type, sK133: $i > $i > $i).
% 2.43/1.58 thf(func_def_243, type, sK134: $i > $i > $i).
% 2.43/1.58 thf(func_def_244, type, sK135: $i > $i > $i).
% 2.43/1.58 thf(func_def_245, type, sK136: $i > $i > $i).
% 2.43/1.58 thf(func_def_246, type, sK137: $i > $i > $i > $i).
% 2.43/1.58 thf(func_def_247, type, sK138: $i > $i).
% 2.43/1.58 thf(func_def_248, type, sK139: $i > $i).
% 2.43/1.58 thf(func_def_249, type, sK140: $i > $i).
% 2.43/1.58 thf(func_def_250, type, sK141: $i > $i).
% 2.43/1.58 thf(func_def_251, type, sK142: $i > $i > $i > $i).
% 2.43/1.58 thf(func_def_252, type, sK143: $i > $i > $i > $i).
% 2.43/1.58 thf(func_def_253, type, sK144: $i > $i > $i).
% 2.43/1.58 thf(func_def_254, type, sK145: $i > $i > $i).
% 2.43/1.58 thf(func_def_255, type, sK146: $i > $i > $i).
% 2.43/1.58 thf(func_def_257, type, sK148: $i > $i).
% 2.43/1.58 thf(func_def_258, type, sK149: $i > $i).
% 2.43/1.58 thf(func_def_259, type, sK150: $i > $i).
% 2.43/1.58 thf(func_def_260, type, sK151: $i > $i > $i).
% 2.43/1.58 thf(func_def_261, type, sK152: $i > $o).
% 2.43/1.58 thf(func_def_263, type, sK154: $i > ($i > $o) > $i).
% 2.43/1.58 thf(func_def_265, type, sK156: $i > $o).
% 2.43/1.58 thf(func_def_267, type, sK158: ($i > $o) > $i > $i).
% 2.43/1.58 thf(func_def_269, type, sK160: $i > $o).
% 2.43/1.58 thf(func_def_271, type, sK162: $i > $o).
% 2.43/1.58 thf(func_def_277, type, sK168: $i > $i > $i).
% 2.43/1.58 thf(func_def_283, type, sK174: $i > $o).
% 2.43/1.58 thf(func_def_285, type, sK176: ($i > $o) > $i > $i).
% 2.43/1.58 thf(func_def_289, type, sK180: $i > $o).
% 2.43/1.58 thf(func_def_291, type, sK182: ($i > $o) > $i).
% 2.43/1.58 thf(func_def_292, type, sK183: ($i > $o) > $i).
% 2.43/1.58 thf(func_def_294, type, sK185: $i > $o).
% 2.43/1.58 thf(func_def_296, type, sK187: $i > $i).
% 2.43/1.58 thf(func_def_298, type, sK189: $i > $i).
% 2.43/1.58 thf(func_def_301, type, sK192: $i > $o).
% 2.43/1.58 thf(func_def_304, type, sK195: $i > $o).
% 2.43/1.58 thf(func_def_305, type, sK196: $i > $o).
% 2.43/1.58 thf(func_def_306, type, sK197: ($i > $o) > ($i > $o) > $i).
% 2.43/1.58 thf(func_def_307, type, sK198: ($i > $o) > ($i > $o) > $i).
% 2.43/1.58 thf(func_def_314, type, sK205: $o > $i > $i > $i).
% 2.43/1.58 thf(func_def_315, type, sK206: $i > $o).
% 2.43/1.58 thf(func_def_318, type, sK209: $i > ($i > $o) > $i).
% 2.43/1.58 thf(func_def_321, type, sK212: $i > $i > $i).
% 2.43/1.58 thf(func_def_329, type, sK220: ($i > $o) > $i > $i).
% 2.43/1.58 thf(func_def_331, type, sK222: $i > $o).
% 2.43/1.58 thf(func_def_347, type, ph238: !>[X0: $tType]:(X0)).
% 2.43/1.58 thf(f1634,plain,(
% 2.43/1.58 $false),
% 2.43/1.58 inference(trivial_inequality_removal,[status(thm)],[f1626])).
% 2.43/1.58 thf(f1626,plain,(
% 2.43/1.58 ($true != $true)),
% 2.43/1.58 inference(superposition,[status(thm)],[f1302,f835])).
% 2.43/1.58 thf(f835,plain,(
% 2.43/1.58 ($true = (in @ sK25 @ sK26))),
% 2.43/1.58 inference(cnf_transformation,[status(thm)],[f401])).
% 2.43/1.58 thf(f401,plain,(
% 2.43/1.58 (setadjoinAx = $true) & (exu__Cong = $true) & (setunionI = $true) & (nonemptyI = $true) & (prop2set2propI = $true) & (setbeta = $true) & (exuE3u = $true) & (powerset__Cong = $true) & (upairsetE = $true) & (exuEu = $true) & (prop2setI = $true) & (exuI1 = $true) & (emptyinunitempty = $true) & (quantDeMorgan3 = $true) & (nonemptyE1 = $true) & (nonemptyI1 = $true) & (setadjoinIR = $true) & (exuE3e = $true) & (notinsingleton = $true) & (setunionAx = $true) & (emptysetsubset = $true) & (nonemptyImpWitness = $true) & (prop2setE = $true) & (setadjoinOr = $true) & (omegaIndAx = $true) & (powersetAx = $true) & (dsetconstr__Cong = $true) & (vacuousDall = $true) & (eqinunit = $true) & (quantDeMorgan1 = $true) & (emptyE1 = $true) & (notdallE = $true) & (emptyI = $true) & (notinemptyset = $true) & (wellorderingAx = $true) & (dsetconstrEL = $true) & (in__Cong = $true) & (descrp = $true) & (foundationAx = $true) & (emptysetE = $true) & (dsetconstrI = $true) & (omega0Ax = $true) & (noeltsimpempty = $true) & (uniqinunit = $true) & (emptysetAx = $true) & (emptyset__Cong = $true) & (setadjoinIL = $true) & (exuI3 = $true) & (subsetE = $true) & (eqimpsubset2 = $true) & (($true != (in @ sK25 @ sK27)) & ($true = (subset @ sK26 @ sK27)) & ($true = (in @ sK25 @ sK26))) & (powersetI = $true) & (notdexE = $true) & (exuE2 = $true) & (setadjoin__Cong = $true) & (dsetconstrER = $true) & (subPowSU = $true) & (setunion__Cong = $true) & (emptysetimpfalse = $true) & (subsetI2 = $true) & (replAx = $true) & (powersetE = $true) & (subsetI1 = $true) & (quantDeMorgan2 = $true) & (singletonsswitch = $true) & (omega__Cong = $true) & (descr__Cong = $true) & (emptyinPowerset = $true) & (setextAx = $true) & (inCongP = $true) & (quantDeMorgan4 = $true) & (setext = $true) & (exuE1 = $true) & (setunionE = $true) & (eqimpsubset1 = $true) & (setoftrueEq = $true) & (upairsetIL = $true) & (upairsetIR = $true) & (omegaSAx = $true) & (emptyInPowerset = $true) & (setadjoinE = $true) & (exuI2 = $true)),
% 2.43/1.58 inference(skolemisation,[status(esa),new_symbols(skolem,[sK25,sK26,sK27])],[f308,f400])).
% 2.43/1.58 thf(f400,plain,(
% 2.43/1.58 ? [X0 : $i,X1 : $i,X2 : $i] : (($true != (in @ X0 @ X2)) & ($true = (subset @ X1 @ X2)) & ($true = (in @ X0 @ X1))) => (($true != (in @ sK25 @ sK27)) & ($true = (subset @ sK26 @ sK27)) & ($true = (in @ sK25 @ sK26)))),
% 2.43/1.58 introduced(definition,[],[choice_axiom])).
% 2.43/1.58 thf(f308,plain,(
% 2.43/1.58 (setadjoinAx = $true) & (exu__Cong = $true) & (setunionI = $true) & (nonemptyI = $true) & (prop2set2propI = $true) & (setbeta = $true) & (exuE3u = $true) & (powerset__Cong = $true) & (upairsetE = $true) & (exuEu = $true) & (prop2setI = $true) & (exuI1 = $true) & (emptyinunitempty = $true) & (quantDeMorgan3 = $true) & (nonemptyE1 = $true) & (nonemptyI1 = $true) & (setadjoinIR = $true) & (exuE3e = $true) & (notinsingleton = $true) & (setunionAx = $true) & (emptysetsubset = $true) & (nonemptyImpWitness = $true) & (prop2setE = $true) & (setadjoinOr = $true) & (omegaIndAx = $true) & (powersetAx = $true) & (dsetconstr__Cong = $true) & (vacuousDall = $true) & (eqinunit = $true) & (quantDeMorgan1 = $true) & (emptyE1 = $true) & (notdallE = $true) & (emptyI = $true) & (notinemptyset = $true) & (wellorderingAx = $true) & (dsetconstrEL = $true) & (in__Cong = $true) & (descrp = $true) & (foundationAx = $true) & (emptysetE = $true) & (dsetconstrI = $true) & (omega0Ax = $true) & (noeltsimpempty = $true) & (uniqinunit = $true) & (emptysetAx = $true) & (emptyset__Cong = $true) & (setadjoinIL = $true) & (exuI3 = $true) & (subsetE = $true) & (eqimpsubset2 = $true) & ? [X0 : $i,X1 : $i,X2 : $i] : (($true != (in @ X0 @ X2)) & ($true = (subset @ X1 @ X2)) & ($true = (in @ X0 @ X1))) & (powersetI = $true) & (notdexE = $true) & (exuE2 = $true) & (setadjoin__Cong = $true) & (dsetconstrER = $true) & (subPowSU = $true) & (setunion__Cong = $true) & (emptysetimpfalse = $true) & (subsetI2 = $true) & (replAx = $true) & (powersetE = $true) & (subsetI1 = $true) & (quantDeMorgan2 = $true) & (singletonsswitch = $true) & (omega__Cong = $true) & (descr__Cong = $true) & (emptyinPowerset = $true) & (setextAx = $true) & (inCongP = $true) & (quantDeMorgan4 = $true) & (setext = $true) & (exuE1 = $true) & (setunionE = $true) & (eqimpsubset1 = $true) & (setoftrueEq = $true) & (upairsetIL = $true) & (upairsetIR = $true) & (omegaSAx = $true) & (emptyInPowerset = $true) & (setadjoinE = $true) & (exuI2 = $true)),
% 2.43/1.58 inference(flattening,[status(thm)],[f307])).
% 2.43/1.58 thf(f307,plain,(
% 2.43/1.58 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((? [X0 : $i,X1 : $i,X2 : $i] : ((($true = (in @ X0 @ X1)) & ($true != (in @ X0 @ X2))) & ($true = (subset @ X1 @ X2))) & (subsetE = $true)) & (emptysetsubset = $true)) & (subsetI2 = $true)) & (eqimpsubset1 = $true)) & (eqimpsubset2 = $true)) & (subsetI1 = $true)) & (dsetconstr__Cong = $true)) & (descr__Cong = $true)) & (exuEu = $true)) & (omega__Cong = $true)) & (setunion__Cong = $true)) & (powerset__Cong = $true)) & (setadjoin__Cong = $true)) & (emptyset__Cong = $true)) & (exu__Cong = $true)) & (exuE3u = $true)) & (in__Cong = $true)) & (inCongP = $true)) & (exuI2 = $true)) & (exuI3 = $true)) & (exuI1 = $true)) & (notdallE = $true)) & (notdexE = $true)) & (prop2set2propI = $true)) & (prop2setI = $true)) & (quantDeMorgan4 = $true)) & (quantDeMorgan3 = $true)) & (quantDeMorgan2 = $true)) & (quantDeMorgan1 = $true)) & (vacuousDall = $true)) & (emptyE1 = $true)) & (upairsetIR = $true)) & (upairsetIL = $true)) & (upairsetE = $true)) & (singletonsswitch = $true)) & (eqinunit = $true)) & (notinsingleton = $true)) & (uniqinunit = $true)) & (nonemptyImpWitness = $true)) & (exuE2 = $true)) & (subPowSU = $true)) & (setunionE = $true)) & (setunionI = $true)) & (powersetE = $true)) & (emptyInPowerset = $true)) & (emptyinPowerset = $true)) & (powersetI = $true)) & (setoftrueEq = $true)) & (setadjoinOr = $true)) & (setadjoinE = $true)) & (setadjoinIR = $true)) & (emptyinunitempty = $true)) & (setadjoinIL = $true)) & (nonemptyI1 = $true)) & (nonemptyI = $true)) & (nonemptyE1 = $true)) & (setbeta = $true)) & (noeltsimpempty = $true)) & (emptyI = $true)) & (setext = $true)) & (exuE3e = $true)) & (notinemptyset = $true)) & (emptysetimpfalse = $true)) & (emptysetE = $true)) & (prop2setE = $true)) & (exuE1 = $true)) & (dsetconstrER = $true)) & (dsetconstrEL = $true)) & (dsetconstrI = $true)) & (descrp = $true)) & (wellorderingAx = $true)) & (foundationAx = $true)) & (replAx = $true)) & (omegaIndAx = $true)) & (omegaSAx = $true)) & (omega0Ax = $true)) & (setunionAx = $true)) & (powersetAx = $true)) & (setadjoinAx = $true)) & (emptysetAx = $true)) & (setextAx = $true)),
% 2.43/1.58 inference(ennf_transformation,[status(thm)],[f268])).
% 2.43/1.58 thf(f268,plain,(
% 2.43/1.58 ~((setextAx = $true) => ((emptysetAx = $true) => ((setadjoinAx = $true) => ((powersetAx = $true) => ((setunionAx = $true) => ((omega0Ax = $true) => ((omegaSAx = $true) => ((omegaIndAx = $true) => ((replAx = $true) => ((foundationAx = $true) => ((wellorderingAx = $true) => ((descrp = $true) => ((dsetconstrI = $true) => ((dsetconstrEL = $true) => ((dsetconstrER = $true) => ((exuE1 = $true) => ((prop2setE = $true) => ((emptysetE = $true) => ((emptysetimpfalse = $true) => ((notinemptyset = $true) => ((exuE3e = $true) => ((setext = $true) => ((emptyI = $true) => ((noeltsimpempty = $true) => ((setbeta = $true) => ((nonemptyE1 = $true) => ((nonemptyI = $true) => ((nonemptyI1 = $true) => ((setadjoinIL = $true) => ((emptyinunitempty = $true) => ((setadjoinIR = $true) => ((setadjoinE = $true) => ((setadjoinOr = $true) => ((setoftrueEq = $true) => ((powersetI = $true) => ((emptyinPowerset = $true) => ((emptyInPowerset = $true) => ((powersetE = $true) => ((setunionI = $true) => ((setunionE = $true) => ((subPowSU = $true) => ((exuE2 = $true) => ((nonemptyImpWitness = $true) => ((uniqinunit = $true) => ((notinsingleton = $true) => ((eqinunit = $true) => ((singletonsswitch = $true) => ((upairsetE = $true) => ((upairsetIL = $true) => ((upairsetIR = $true) => ((emptyE1 = $true) => ((vacuousDall = $true) => ((quantDeMorgan1 = $true) => ((quantDeMorgan2 = $true) => ((quantDeMorgan3 = $true) => ((quantDeMorgan4 = $true) => ((prop2setI = $true) => ((prop2set2propI = $true) => ((notdexE = $true) => ((notdallE = $true) => ((exuI1 = $true) => ((exuI3 = $true) => ((exuI2 = $true) => ((inCongP = $true) => ((in__Cong = $true) => ((exuE3u = $true) => ((exu__Cong = $true) => ((emptyset__Cong = $true) => ((setadjoin__Cong = $true) => ((powerset__Cong = $true) => ((setunion__Cong = $true) => ((omega__Cong = $true) => ((exuEu = $true) => ((descr__Cong = $true) => ((dsetconstr__Cong = $true) => ((subsetI1 = $true) => ((eqimpsubset2 = $true) => ((eqimpsubset1 = $true) => ((subsetI2 = $true) => ((emptysetsubset = $true) => ((subsetE = $true) => ! [X0 : $i,X1 : $i,X2 : $i] : (($true = (subset @ X1 @ X2)) => (($true != (in @ X0 @ X2)) => ($true != (in @ X0 @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 2.43/1.58 inference(flattening,[status(thm)],[f233])).
% 2.43/1.58 thf(f233,plain,(
% 2.43/1.58 ~((setextAx = $true) => ((emptysetAx = $true) => ((setadjoinAx = $true) => ((powersetAx = $true) => ((setunionAx = $true) => ((omega0Ax = $true) => ((omegaSAx = $true) => ((omegaIndAx = $true) => ((replAx = $true) => ((foundationAx = $true) => ((wellorderingAx = $true) => ((descrp = $true) => ((dsetconstrI = $true) => ((dsetconstrEL = $true) => ((dsetconstrER = $true) => ((exuE1 = $true) => ((prop2setE = $true) => ((emptysetE = $true) => ((emptysetimpfalse = $true) => ((notinemptyset = $true) => ((exuE3e = $true) => ((setext = $true) => ((emptyI = $true) => ((noeltsimpempty = $true) => ((setbeta = $true) => ((nonemptyE1 = $true) => ((nonemptyI = $true) => ((nonemptyI1 = $true) => ((setadjoinIL = $true) => ((emptyinunitempty = $true) => ((setadjoinIR = $true) => ((setadjoinE = $true) => ((setadjoinOr = $true) => ((setoftrueEq = $true) => ((powersetI = $true) => ((emptyinPowerset = $true) => ((emptyInPowerset = $true) => ((powersetE = $true) => ((setunionI = $true) => ((setunionE = $true) => ((subPowSU = $true) => ((exuE2 = $true) => ((nonemptyImpWitness = $true) => ((uniqinunit = $true) => ((notinsingleton = $true) => ((eqinunit = $true) => ((singletonsswitch = $true) => ((upairsetE = $true) => ((upairsetIL = $true) => ((upairsetIR = $true) => ((emptyE1 = $true) => ((vacuousDall = $true) => ((quantDeMorgan1 = $true) => ((quantDeMorgan2 = $true) => ((quantDeMorgan3 = $true) => ((quantDeMorgan4 = $true) => ((prop2setI = $true) => ((prop2set2propI = $true) => ((notdexE = $true) => ((notdallE = $true) => ((exuI1 = $true) => ((exuI3 = $true) => ((exuI2 = $true) => ((inCongP = $true) => ((in__Cong = $true) => ((exuE3u = $true) => ((exu__Cong = $true) => ((emptyset__Cong = $true) => ((setadjoin__Cong = $true) => ((powerset__Cong = $true) => ((setunion__Cong = $true) => ((omega__Cong = $true) => ((exuEu = $true) => ((descr__Cong = $true) => ((dsetconstr__Cong = $true) => ((subsetI1 = $true) => ((eqimpsubset2 = $true) => ((eqimpsubset1 = $true) => ((subsetI2 = $true) => ((emptysetsubset = $true) => ((subsetE = $true) => ! [X0 : $i,X1 : $i,X2 : $i] : (($true = (subset @ X1 @ X2)) => (~($true = (in @ X0 @ X2)) => ~($true = (in @ X0 @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 2.43/1.58 inference(fool_elimination,[status(thm)],[f232])).
% 2.43/1.58 thf(f232,plain,(
% 2.43/1.58 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => ! [X0 : $i,X1 : $i,X2 : $i] : ((subset @ X1 @ X2) => (~(in @ X0 @ X2) => ~(in @ X0 @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 2.43/1.58 inference(rectify,[status(thm)],[f85])).
% 2.43/1.58 thf(f85,negated_conjecture,(
% 2.43/1.58 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => ! [X1 : $i,X3 : $i,X4 : $i] : ((subset @ X3 @ X4) => (~(in @ X1 @ X4) => ~(in @ X1 @ X3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 2.43/1.58 inference(negated_conjecture,[status(cth)],[f84])).
% 2.43/1.58 thf(f84,conjecture,(
% 2.43/1.58 setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => ! [X1 : $i,X3 : $i,X4 : $i] : ((subset @ X3 @ X4) => (~(in @ X1 @ X4) => ~(in @ X1 @ X3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 2.43/1.58 file('/export/starexec/sandbox2/tmp/tmp.cd1eMribCG/DTF2THF_26070.p',subsetE2)).
% 2.43/1.58 thf(f1302,plain,(
% 2.43/1.58 ($true != (in @ sK25 @ sK26))),
% 2.43/1.58 inference(trivial_inequality_removal,[status(thm)],[f1296])).
% 2.43/1.58 thf(f1296,plain,(
% 2.43/1.58 ($true != (in @ sK25 @ sK26)) | ($true != $true)),
% 2.43/1.58 inference(superposition,[status(thm)],[f1295,f836])).
% 2.43/1.58 thf(f836,plain,(
% 2.43/1.58 ($true = (subset @ sK26 @ sK27))),
% 2.43/1.58 inference(cnf_transformation,[status(thm)],[f401])).
% 2.43/1.58 thf(f1295,plain,(
% 2.43/1.58 ( ! [X0 : $i] : (($true != (subset @ X0 @ sK27)) | ($true != (in @ sK25 @ X0))) )),
% 2.43/1.58 inference(trivial_inequality_removal,[status(thm)],[f1294])).
% 2.43/1.58 thf(f1294,plain,(
% 2.43/1.58 ( ! [X0 : $i] : (($true != (subset @ X0 @ sK27)) | ($true != (in @ sK25 @ X0)) | ($true != $true)) )),
% 2.43/1.58 inference(forward_demodulation,[status(thm)],[f1293,f839])).
% 2.43/1.58 thf(f839,plain,(
% 2.43/1.58 (subsetE = $true)),
% 2.43/1.58 inference(cnf_transformation,[status(thm)],[f401])).
% 2.43/1.58 thf(f1293,plain,(
% 2.43/1.58 ( ! [X0 : $i] : (($true != (in @ sK25 @ X0)) | ($true != (subset @ X0 @ sK27)) | (subsetE != $true)) )),
% 2.43/1.58 inference(trivial_inequality_removal,[status(thm)],[f1290])).
% 2.43/1.58 thf(f1290,plain,(
% 2.43/1.58 ( ! [X0 : $i] : (($true != (subset @ X0 @ sK27)) | (subsetE != $true) | ($true != (in @ sK25 @ X0)) | ($true != $true)) )),
% 2.43/1.58 inference(superposition,[status(thm)],[f837,f1035])).
% 2.43/1.58 thf(f1035,plain,(
% 2.43/1.58 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X3 @ X4) = $true) | ($true != (in @ X3 @ X5)) | (subsetE != $true) | ($true != (subset @ X5 @ X4))) )),
% 2.43/1.58 inference(cnf_transformation,[status(thm)],[f585])).
% 2.43/1.58 thf(f585,plain,(
% 2.43/1.58 ((subsetE = $true) | (($true = (in @ sK125 @ sK127)) & ($true != (in @ sK125 @ sK126)) & ($true = (subset @ sK127 @ sK126)))) & (! [X3 : $i,X4 : $i,X5 : $i] : (($true != (in @ X3 @ X5)) | ((in @ X3 @ X4) = $true) | ($true != (subset @ X5 @ X4))) | (subsetE != $true))),
% 2.43/1.58 inference(skolemisation,[status(esa),new_symbols(skolem,[sK125,sK126,sK127])],[f583,f584])).
% 2.43/1.58 thf(f584,plain,(
% 2.43/1.58 ? [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X0 @ X2)) & ($true != (in @ X0 @ X1)) & ((subset @ X2 @ X1) = $true)) => (($true = (in @ sK125 @ sK127)) & ($true != (in @ sK125 @ sK126)) & ($true = (subset @ sK127 @ sK126)))),
% 2.43/1.58 introduced(definition,[],[choice_axiom])).
% 2.43/1.58 thf(f583,plain,(
% 2.43/1.58 ((subsetE = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X0 @ X2)) & ($true != (in @ X0 @ X1)) & ((subset @ X2 @ X1) = $true))) & (! [X3 : $i,X4 : $i,X5 : $i] : (($true != (in @ X3 @ X5)) | ((in @ X3 @ X4) = $true) | ($true != (subset @ X5 @ X4))) | (subsetE != $true))),
% 2.43/1.58 inference(rectify,[status(thm)],[f582])).
% 2.43/1.58 thf(f582,plain,(
% 2.43/1.58 ((subsetE = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X0 @ X2)) & ($true != (in @ X0 @ X1)) & ((subset @ X2 @ X1) = $true))) & (! [X0 : $i,X1 : $i,X2 : $i] : (($true != (in @ X0 @ X2)) | ($true = (in @ X0 @ X1)) | ((subset @ X2 @ X1) != $true)) | (subsetE != $true))),
% 2.43/1.58 inference(nnf_transformation,[status(thm)],[f284])).
% 2.43/1.58 thf(f284,plain,(
% 2.43/1.58 (subsetE = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (($true != (in @ X0 @ X2)) | ($true = (in @ X0 @ X1)) | ((subset @ X2 @ X1) != $true))),
% 2.43/1.58 inference(flattening,[status(thm)],[f283])).
% 2.43/1.58 thf(f283,plain,(
% 2.43/1.58 (subsetE = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : ((($true = (in @ X0 @ X1)) | ($true != (in @ X0 @ X2))) | ((subset @ X2 @ X1) != $true))),
% 2.43/1.58 inference(ennf_transformation,[status(thm)],[f179])).
% 2.43/1.58 thf(f179,plain,(
% 2.43/1.58 (subsetE = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (((subset @ X2 @ X1) = $true) => (($true = (in @ X0 @ X2)) => ($true = (in @ X0 @ X1))))),
% 2.43/1.58 inference(fool_elimination,[status(thm)],[f178])).
% 2.43/1.58 thf(f178,plain,(
% 2.43/1.58 (! [X0 : $i,X1 : $i,X2 : $i] : ((subset @ X2 @ X1) => ((in @ X0 @ X2) => (in @ X0 @ X1))) = subsetE)),
% 2.43/1.58 inference(rectify,[status(thm)],[f83])).
% 2.43/1.58 thf(f83,axiom,(
% 2.43/1.58 (! [X1 : $i,X4 : $i,X3 : $i] : ((subset @ X3 @ X4) => ((in @ X1 @ X3) => (in @ X1 @ X4))) = subsetE)),
% 2.43/1.58 file('/export/starexec/sandbox2/tmp/tmp.cd1eMribCG/DTF2THF_26070.p',subsetE)).
% 2.43/1.58 thf(f837,plain,(
% 2.43/1.58 ($true != (in @ sK25 @ sK27))),
% 2.43/1.58 inference(cnf_transformation,[status(thm)],[f401])).
% 2.43/1.58 % SZS output end Proof for DTF2THF_26070
% 2.43/1.58 % (26355)------------------------------
% 2.43/1.58 % (26355)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.43/1.58 % (26355)Termination reason: Refutation
% 2.43/1.58
% 2.43/1.58 % (26355)Memory used [KB]: 7036
% 2.43/1.58 % (26355)Time elapsed: 0.048 s
% 2.43/1.58 % (26355)Instructions burned: 131 (million)
% 2.43/1.58 % (26355)------------------------------
% 2.43/1.58 % (26355)------------------------------
% 2.43/1.58 % (26293)Success in time 0.118 s
%------------------------------------------------------------------------------